Daily Papers

We ask whether pretrained time series foundation models (TSFMs) improve on established econometric benchmarks for forecasting realized volatility. Using the VOLARE dataset, we conduct the first systematic comparison of nine zero-shot TSFMs against eight econometric specifications, including the Heterogeneous Autoregressive (HAR) family, across 50 assets in equities, foreign exchange, and futures, and three forecast horizons, with formal pairwise and multi-model forecast-comparison tests. Foundation models do not deliver a uniform gain. Pooled losses favor them, but the advantage is concentrated in a few outlier assets; averaging each asset's loss ratio to a well-specified Log-HAR benchmark, so that no single asset dominates, only one small model, Tiny Time Mixers (TTM), beats the benchmark at every horizon, and by a narrow margin. The other foundation models do not improve on Log-HAR, and the econometric benchmarks remain competitive throughout. A Mincer--Zarnowitz recalibration, which removes level and scale bias from every forecast, shows that much of the short-horizon advantage reflects better-scaled forecasts rather than better prediction of volatility dynamics, and only at the monthly horizon does a genuine informational gain remain. Because this edge is thin and even TTM is not best on every asset, a simple equal-weight average of TTM and Log-HAR matches the best single model and enters the Model Confidence Set for 98 to 100\% of assets, more often than either component alone, so a forecaster need not identify the best model for each asset in advance. Our most durable finding is that performance varies so much across foundation-model architectures that choosing the right architecture matters more than the broader choice between foundation and econometric models.

Many empirical studies of labor market questions rely on estimating relatively simple predictive models using small, carefully constructed longitudinal survey datasets based on hand-engineered features. Large Language Models (LLMs), trained on massive datasets, encode vast quantities of world knowledge and can be used for the next job prediction problem. However, while an off-the-shelf LLM produces plausible career trajectories when prompted, the probability with which an LLM predicts a particular job transition conditional on career history will not, in general, align with the true conditional probability in a given population. Recently, Vafa et al. (2024) introduced a transformer-based "foundation model", CAREER, trained using a large, unrepresentative resume dataset, that predicts transitions between jobs; it further demonstrated how transfer learning techniques can be used to leverage the foundation model to build better predictive models of both transitions and wages that reflect conditional transition probabilities found in nationally representative survey datasets. This paper considers an alternative where the fine-tuning of the CAREER foundation model is replaced by fine-tuning LLMs. For the task of next job prediction, we demonstrate that models trained with our approach outperform several alternatives in terms of predictive performance on the survey data, including traditional econometric models, CAREER, and LLMs with in-context learning, even though the LLM can in principle predict job titles that are not allowed in the survey data. Further, we show that our fine-tuned LLM-based models' predictions are more representative of the career trajectories of various workforce subpopulations than off-the-shelf LLM models and CAREER. We conduct experiments and analyses that highlight the sources of the gains in the performance of our models for representative predictions.

This study develops FinText, a financial word embedding compiled from 15 years of business news archives. The results show that FinText produces substantially more accurate results than general word embeddings based on the gold-standard financial benchmark we introduced. In contrast to well-known econometric models, and over the sample period from 27 July 2007 to 27 January 2022 for 23 NASDAQ stocks, using stock-related news, our simple natural language processing model supported by different word embeddings improves realised volatility forecasts on high volatility days. This improvement in realised volatility forecasting performance switches to normal volatility days when general hot news is used. By utilising SHAP, an Explainable AI method, we also identify and classify key phrases in stock-related and general hot news that moved volatility.

This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student's t, and skewed Student's t. Using custom negative log-likelihood loss functions, distribution parameters are optimized directly. The models are tested on six major equity indices (S\&P 500, BOVESPA, DAX, WIG, Nikkei 225, and KOSPI) using probabilistic evaluation metrics including Log Predictive Score (LPS), Continuous Ranked Probability Score (CRPS), and Probability Integral Transform (PIT). Results show that deep learning models provide accurate distributional forecasts and perform competitively with classical GARCH models for Value-at-Risk estimation. The LSTM with skewed Student's t distribution performs best across multiple evaluation criteria, capturing both heavy tails and asymmetry in financial returns. This work shows that deep neural networks are viable alternatives to traditional econometric models for financial risk assessment and portfolio management.

Artificial intelligence is transforming financial investment decision-making frameworks, with deep reinforcement learning demonstrating substantial potential in robo-advisory applications. This paper addresses the limitations of traditional portfolio optimization methods in dynamic asset weight adjustment through the development of a deep reinforcement learning-based dynamic optimization model grounded in practical trading processes. The research advances two key innovations: first, the introduction of a novel Sharpe ratio reward function engineered for Actor-Critic deep reinforcement learning algorithms, which ensures stable convergence during training while consistently achieving positive average Sharpe ratios; second, the development of an innovative comprehensive approach to portfolio optimization utilizing deep reinforcement learning, which significantly enhances model optimization capability through the integration of random sampling strategies during training with image-based deep neural network architectures for multi-dimensional financial time series data processing, average Sharpe ratio reward functions, and deep reinforcement learning algorithms. The empirical analysis validates the model using randomly selected constituent stocks from the CSI 300 Index, benchmarking against established financial econometric optimization models. Backtesting results demonstrate the model's efficacy in optimizing portfolio allocation and mitigating investment risk, yielding superior comprehensive performance metrics.

For a long-time, researchers have been developing a reliable and accurate predictive model for stock price prediction. According to the literature, if predictive models are correctly designed and refined, they can painstakingly and faithfully estimate future stock values. This paper demonstrates a set of time series, econometric, and various learning-based models for stock price prediction. The data of Infosys, ICICI, and SUN PHARMA from the period of January 2004 to December 2019 was used here for training and testing the models to know which model performs best in which sector. One time series model (Holt-Winters Exponential Smoothing), one econometric model (ARIMA), two machine Learning models (Random Forest and MARS), and two deep learning-based models (simple RNN and LSTM) have been included in this paper. MARS has been proved to be the best performing machine learning model, while LSTM has proved to be the best performing deep learning model. But overall, for all three sectors - IT (on Infosys data), Banking (on ICICI data), and Health (on SUN PHARMA data), MARS has proved to be the best performing model in sales forecasting.

We develop an econometric framework integrating heavy-tailed Student's t distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we demonstrate Student's t specifications outperform Gaussian models in 88.4\% of cases. Bounded probability-weighting transformations preserve mathematical properties required for dynamic pricing. Gaussian models underestimate 99\% Value-at-Risk by 19.7\% versus 3.2\% for our specification. Joint estimation procedures identify tail and behavioral parameters with established asymptotic properties. Results provide robust inference for asset-pricing applications where heavy tails and behavioral distortions coexist.

In this paper, we develop a hybrid approach to forecasting the volatility and risk of financial instruments by combining common econometric GARCH time series models with deep learning neural networks. For the latter, we employ Gated Recurrent Unit (GRU) networks, whereas four different specifications are used as the GARCH component: standard GARCH, EGARCH, GJR-GARCH and APARCH. Models are tested using daily logarithmic returns on the S&P 500 index as well as gold price Bitcoin prices, with the three assets representing quite distinct volatility dynamics. As the main volatility estimator, also underlying the target function of our hybrid models, we use the price-range-based Garman-Klass estimator, modified to incorporate the opening and closing prices. Volatility forecasts resulting from the hybrid models are employed to evaluate the assets' risk using the Value-at-Risk (VaR) and Expected Shortfall (ES) at two different tolerance levels of 5% and 1%. Gains from combining the GARCH and GRU approaches are discussed in the contexts of both the volatility and risk forecasts. In general, it can be concluded that the hybrid solutions produce more accurate point volatility forecasts, although it does not necessarily translate into superior VaR and ES forecasts.

The debate around misinformation and its potentially detrimental effects on public opinion is complex and multifaceted, to the extent that even the relevant academic research has not found unanimity on the prevalence and consumption of misinformation compared with mainstream content. The methodological framework presented here emphasises the importance of considering data representative of the complexity of the phenomenon and metrics that control for possible scale effects. By combining statistical, econometric and machine learning models, we shed light on the real impact of misinformation about a subject of general interest and social relevance, such as vaccines, on both the information available to citizens and their news diet. Our results show the prominent role achieved by misinformation sources in the news ecosystem, but also - and above all - the inability of mainstream media to drive the public debate over time on issues that are particularly sensitive and emotional. Taking properly account for the temporal dynamics of public debate seems crucial to prevent the latter from moving into uncontrolled spaces where false narratives are more easily conveyed and entrenched.

We show how state-of-the-art large language models (LLMs) can be trained effectively on limited historical data for macroeconomic forecasting. We estimate a dynamic stochastic general equilibrium (DSGE) model with stochastic volatility and Student-t shocks on an initial segment of the data to obtain a posterior distribution over structural parameters. We sample from this posterior to generate millions of theory-consistent synthetic panels that, when mixed with macroeconomic data, form the training corpus for a deep learning transformer. Rather than using the DSGE model as a direct forecasting device, we use it as a structural simulator that regularizes transformer training in a small-sample environment. Our results show that this hybrid forecaster, which combines the theoretical coherence of DSGE models with the representational power of modern LLMs, learns key features of the macroeconomic language. Relative to a conventional vector autoregression benchmark, the transformer achieves comparable or stronger predictive performance in both token accuracy and predictive likelihood. These gains are strongest under a theory-heavy training mix and remain broadly robust to finer tokenization and deeper network architecture.

Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, determination of liability, and policy analysis. We present a method of revaluating counterfactuals when the underlying causal model is represented by structural models - a nonlinear generalization of the simultaneous equations models commonly used in econometrics and social sciences. This new method provides a coherent means for evaluating policies involving the control of variables which, prior to enacting the policy were influenced by other variables in the system.

This research employs quantitative techniques interpreted through relevant economic theories to analyze a proposed U.S. "Discounted Reciprocal Tariff" structure. Statistical modeling (linear regression) quantifies the policy's consistent 'discounted reciprocity' pattern, which is interpreted using a Game Theory perspective on strategic interaction. Machine learning (K-Means clustering) identifies distinct country typologies based on tariff exposure and Economic Complexity Index (ECI), linking the policy to Economic Complexity theory. The study's primary application focuses on the major coffee exporting sector, utilizing simulation modeling grounded in principles of demand elasticity and substitution to project potential trade flow impacts. Specifically, for coffee, this simulation demonstrates how the proposed tariff differentials can induce significant substitution effects, projecting a potential shift in U.S. import demand away from high-tariff origins toward lower-tariff competitors. This disruption, stemming from the tariffs impacting exporting countries, is projected to ultimately increase coffee prices for consumers in the United States. Findings throughout are contextualized within Political Economy considerations. Overall, the study demonstrates how integrating regression, clustering, and simulation with economic theory exemplified through the coffee sector analysis provides a robust framework for assessing the potential systemic impacts, including consumer price effects, of strategic trade policies.

This paper examines the fiscal and macroeconomic strategies essential for transition of India to a high income economy by 2047, aligning with the vision of Viksit Bharat. A sustainable annual GDP growth rate of 7 to 8 percent is projected as necessary to achieve this milestone while maintaining fiscal prudence through a targeted deficit threshold below 3.5 percent of GDP. The study underscores the role of disciplined fiscal management in financing critical public investments in infrastructure, human capital development and technological innovation. Given constraints on domestic resource mobilization, the paper highlights the importance of multilateral financial institutions, including the World Bank, IMF and ADB, in expanding fiscal space in India through concessional financing, technical cooperation, and risk sharing mechanisms. Using econometric modeling and scenario analysis, the research identifies key policy interventions in infrastructure, healthcare, education and sustainable energy that can maximize growth while ensuring fiscal sustainability. Policy recommendations include enhancing tax buoyancy, rationalizing expenditure, optimizing public private partnerships and strengthening fiscal responsibility frameworks. The findings suggest that a calibrated approach to growth, prudent fiscal management and strategic international collaborations are critical to achieving long term economic aspirations of India.

Macroeconomic data is characterized by a limited number of observations (small T), many time series (big K) but also by featuring temporal dependence. Neural networks, by contrast, are designed for datasets with millions of observations and covariates. In this paper, we develop Bayesian neural networks (BNNs) that are well-suited for handling datasets commonly used for macroeconomic analysis in policy institutions. Our approach avoids extensive specification searches through a novel mixture specification for the activation function that appropriately selects the form of nonlinearities. Shrinkage priors are used to prune the network and force irrelevant neurons to zero. To cope with heteroskedasticity, the BNN is augmented with a stochastic volatility model for the error term. We illustrate how the model can be used in a policy institution by first showing that our different BNNs produce precise density forecasts, typically better than those from other machine learning methods. Finally, we showcase how our model can be used to recover nonlinearities in the reaction of macroeconomic aggregates to financial shocks.

We propose a multicountry quantile factor augmeneted vector autoregression (QFAVAR) to model heterogeneities both across countries and across characteristics of the distributions of macroeconomic time series. The presence of quantile factors allows for summarizing these two heterogeneities in a parsimonious way. We develop two algorithms for posterior inference that feature varying level of trade-off between estimation precision and computational speed. Using monthly data for the euro area, we establish the good empirical properties of the QFAVAR as a tool for assessing the effects of global shocks on country-level macroeconomic risks. In particular, QFAVAR short-run tail forecasts are more accurate compared to a FAVAR with symmetric Gaussian errors, as well as univariate quantile autoregressions that ignore comovements among quantiles of macroeconomic variables. We also illustrate how quantile impulse response functions and quantile connectedness measures, resulting from the new model, can be used to implement joint risk scenario analysis.

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality: heterogeneous-agent economies, overlapping-generations models with aggregate risk, continuous-time models with occasionally binding constraints, climate-economy models, and macro-finance environments with many assets and frictions generate state and parameter spaces that strain classical tensor-product grid methods. The exposition is organized around four complementary methodologies. Deep Equilibrium Nets embed discrete-time equilibrium conditions into neural-network loss functions. Physics-Informed Neural Networks approximate continuous-time Hamilton--Jacobi--Bellman, Kolmogorov forward, and related partial differential equations. Deep surrogate models provide fast, differentiable approximations to expensive structural models, while Gaussian processes add a probabilistic layer that quantifies approximation uncertainty; together they support estimation, sensitivity analysis, and constrained policy design. Gaussian-process-based dynamic programming, combined with active learning and dimension reduction, extends value-function iteration to very large continuous state spaces. Applications span representative-agent and international real business cycle models, overlapping-generations and heterogeneous-agent economies, continuous-time macro-finance, structural estimation by simulated method of moments, and climate economics under uncertainty. Companion notebooks in TensorFlow and PyTorch invite hands-on experimentation. These notes are a deliberately subjective and inevitably incomplete snapshot of a rapidly evolving field, aimed at equipping PhD students and researchers to engage with this frontier hands-on.

Newly-developed large language models (LLM) -- because of how they are trained and designed -- are implicit computational models of humans -- a homo silicus. These models can be used the same way economists use homo economicus: they can be given endowments, information, preferences, and so on and then their behavior can be explored in scenarios via simulation. I demonstrate this approach using OpenAI's GPT3 with experiments derived from Charness and Rabin (2002), Kahneman, Knetsch and Thaler (1986) and Samuelson and Zeckhauser (1988). The findings are qualitatively similar to the original results, but it is also trivially easy to try variations that offer fresh insights. Departing from the traditional laboratory paradigm, I also create a hiring scenario where an employer faces applicants that differ in experience and wage ask and then analyze how a minimum wage affects realized wages and the extent of labor-labor substitution.

The paper studies the linear model for Bitcoin price which includes regression features based on Bitcoin currency statistics, mining processes, Google search trends, Wikipedia pages visits. The pattern of deviation of regression model prediction from real prices is simpler comparing to price time series. It is assumed that this pattern can be predicted by an experienced expert. In such a way, using the combination of the regression model and expert correction, one can receive better results than with either regression model or expert opinion only. It is shown that Bayesian approach makes it possible to utilize the probabilistic approach using distributions with fat tails and take into account the outliers in Bitcoin price time series.

Most economic theories typically assume that financial market participants are fully rational individuals and use mathematical models to simulate human behavior in financial markets. However, human behavior is often not entirely rational and is challenging to predict accurately with mathematical models. In this paper, we propose Agent-based Simulated Financial Market (ASFM), which first constructs a simulated stock market with a real order matching system. Then, we propose a large language model based agent as the stock trader, which contains the profile, observation, and tool-learning based action module. The trading agent can comprehensively understand current market dynamics and financial policy information, and make decisions that align with their trading strategy. In the experiments, we first verify that the reactions of our ASFM are consistent with the real stock market in two controllable scenarios. In addition, we also conduct experiments in two popular economics research directions, and we find that conclusions drawn in our \model align with the preliminary findings in economics research. Based on these observations, we believe our proposed ASFM provides a new paradigm for economic research.

Covariates provide valuable information on external factors that influence time series and are critical in many real-world time series forecasting tasks. For example, in retail, covariates may indicate promotions or peak dates such as holiday seasons that heavily influence demand forecasts. Recent advances in pretraining large language model architectures for time series forecasting have led to highly accurate forecasters. However, the majority of these models do not readily use covariates as they are often specific to a certain task or domain. This paper introduces a new method to incorporate covariates into pretrained time series forecasting models. Our proposed approach incorporates covariate information into pretrained forecasting models through modular blocks that inject past and future covariate information, without necessarily modifying the pretrained model in consideration. In order to evaluate our approach, we introduce a benchmark composed of 32 different synthetic datasets with varying dynamics to evaluate the effectivity of forecasting models with covariates. Extensive evaluations on both synthetic and real datasets show that our approach effectively incorporates covariate information into pretrained models, outperforming existing baselines.

The Growth-at-Risk (GaR) framework has garnered attention in recent econometric literature, yet current approaches implicitly assume a constant Pareto exponent. We introduce novel and robust econometrics to estimate the tails of GaR based on a rigorous theoretical framework and establish validity and effectiveness. Simulations demonstrate consistent outperformance relative to existing alternatives in terms of predictive accuracy. We perform a long-term GaR analysis that provides accurate and insightful predictions, effectively capturing financial anomalies better than current methods.

In this review, we present econometric and statistical methods for analyzing randomized experiments. For basic experiments we stress randomization-based inference as opposed to sampling-based inference. In randomization-based inference, uncertainty in estimates arises naturally from the random assignment of the treatments, rather than from hypothesized sampling from a large population. We show how this perspective relates to regression analyses for randomized experiments. We discuss the analyses of stratified, paired, and clustered randomized experiments, and we stress the general efficiency gains from stratification. We also discuss complications in randomized experiments such as non-compliance. In the presence of non-compliance we contrast intention-to-treat analyses with instrumental variables analyses allowing for general treatment effect heterogeneity. We consider in detail estimation and inference for heterogeneous treatment effects in settings with (possibly many) covariates. These methods allow researchers to explore heterogeneity by identifying subpopulations with different treatment effects while maintaining the ability to construct valid confidence intervals. We also discuss optimal assignment to treatment based on covariates in such settings. Finally, we discuss estimation and inference in experiments in settings with interactions between units, both in general network settings and in settings where the population is partitioned into groups with all interactions contained within these groups.

Economic World Models (EWMs) are generative economic models that simulate how economies evolve from within by modeling heterogeneous agents, their beliefs and actions, and the market and institutional mechanisms through which their interactions produce aggregate outcomes. This paper develops an implementation roadmap for building economic world models as generative engines in which heterogeneous agents act, interact, adapt, and co-evolve with markets and institutions, thereby producing economic dynamics from the inside. We organize EWM systems into a six-level capability ladder, from fixed rule-based agent worlds to adaptive and LLM-based agent worlds, self-evolving agents, evolving institutional worlds, and sim-to-real economic twins aligned with real observations. A systematic literature survey across these levels reveals that existing work remains concentrated in lower-level agent and simulation environments, while systems with self-evolving agents, endogenous institutions, persistent empirical alignment, and validated economic mechanisms remain rare. By translating the EWM agenda into an implementation blueprint, this paper aims to accelerate the development of the next generation of economic simulation environments that can serve as high-fidelity sandboxes for human decision-makers and as training, planning, evaluation, and safety substrates for AI agents. We release a curated paper list and related resources to support future research.

Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph G=(V, D,B) is parameterized by a rational function with parameters for each vertex and edge in G. This rational parametrization naturally allows for the study of these models from an algebraic and combinatorial point of view. Indeed, this point of view has led to a collection of results in the literature, mainly focusing on questions related to identifiability and determining relationships between covariances (i.e., finding polynomials in the Gaussian vanishing ideal). So far, a large proportion of these results has focused on the case when D, the directed part of the mixed graph G, is acyclic. This is due to the fact that in the acyclic case, the parametrization becomes polynomial and there is a description of the entries of the covariance matrices in terms of a finite sum. We move beyond the acyclic case and give a closed form expression for the entries of the covariance matrices in terms of the one-connections in a graph obtained from D through some small operations. This closed form expression then allows us to show that if G is simple, then the parametrization map is generically finite-to-one. Finally, having a closed form expression for the covariance matrices allows for the development of an algorithm for systematically exploring possible polynomials in the Gaussian vanishing ideal.

We study the problem of model selection in causal inference, specifically for the case of conditional average treatment effect (CATE) estimation under binary treatments. Unlike model selection in machine learning, there is no perfect analogue of cross-validation as we do not observe the counterfactual potential outcome for any data point. Towards this, there have been a variety of proxy metrics proposed in the literature, that depend on auxiliary nuisance models estimated from the observed data (propensity score model, outcome regression model). However, the effectiveness of these metrics has only been studied on synthetic datasets as we can access the counterfactual data for them. We conduct an extensive empirical analysis to judge the performance of these metrics introduced in the literature, and novel ones introduced in this work, where we utilize the latest advances in generative modeling to incorporate multiple realistic datasets. Our analysis suggests novel model selection strategies based on careful hyperparameter tuning of CATE estimators and causal ensembling.

We introduce a novel framework for simulating macroeconomic expectation formation using Large Language Model-Empowered Agents (LLM Agents). By constructing thousands of LLM Agents equipped with modules for personal characteristics, prior expectations, and knowledge, we replicate a survey experiment involving households and experts on inflation and unemployment. Our results show that although the expectations and thoughts generated by LLM Agents are more homogeneous than those of human participants, they still effectively capture key heterogeneity across agents and the underlying drivers of expectation formation. Furthermore, a module-ablation exercise highlights the critical role of prior expectations in simulating such heterogeneity. This approach complements traditional survey methods and offers new insights into AI behavioral science in macroeconomic research.

We initiate the study of statistical inference and A/B testing for first-price pacing equilibria (FPPE). The FPPE model captures the dynamics resulting from large-scale first-price auction markets where buyers use pacing-based budget management. Such markets arise in the context of internet advertising, where budgets are prevalent. We propose a statistical framework for the FPPE model, in which a limit FPPE with a continuum of items models the long-run steady-state behavior of the auction platform, and an observable FPPE consisting of a finite number of items provides the data to estimate primitives of the limit FPPE, such as revenue, Nash social welfare (a fair metric of efficiency), and other parameters of interest. We develop central limit theorems and asymptotically valid confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of our estimators. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Numerical simulations verify our central limit theorems, and empirical coverage rates for our confidence intervals agree with our theory.

International trade policies have recently garnered attention for limiting cross-border exchange of essential goods (e.g. steel, aluminum, soybeans, and beef). Since trade critically affects employment and wages, predicting future patterns of trade is a high-priority for policy makers around the world. While traditional economic models aim to be reliable predictors, we consider the possibility that Machine Learning (ML) techniques allow for better predictions to inform policy decisions. Open-government data provide the fuel to power the algorithms that can explain and forecast trade flows to inform policies. Data collected in this article describe international trade transactions and commonly associated economic factors. Machine learning (ML) models deployed include: ARIMA, GBoosting, XGBoosting, and LightGBM for predicting future trade patterns, and K-Means clustering of countries according to economic factors. Unlike short-term and subjective (straight-line) projections and medium-term (aggre-gated) projections, ML methods provide a range of data-driven and interpretable projections for individual commodities. Models, their results, and policies are introduced and evaluated for prediction quality.

Many applications involve estimating the mean of multiple binomial outcomes as a common problem -- assessing intergenerational mobility of census tracts, estimating prevalence of infectious diseases across countries, and measuring click-through rates for different demographic groups. The most standard approach is to report the plain average of each outcome. Despite simplicity, the estimates are noisy when the sample sizes or mean parameters are small. In contrast, the Empirical Bayes (EB) methods are able to boost the average accuracy by borrowing information across tasks. Nevertheless, the EB methods require a Bayesian model where the parameters are sampled from a prior distribution which, unlike the commonly-studied Gaussian case, is unidentified due to discreteness of binomial measurements. Even if the prior distribution is known, the computation is difficult when the sample sizes are heterogeneous as there is no simple joint conjugate prior for the sample size and mean parameter. In this paper, we consider the compound decision framework which treats the sample size and mean parameters as fixed quantities. We develop an approximate Stein's Unbiased Risk Estimator (SURE) for the average mean squared error given any class of estimators. For a class of machine learning-assisted linear shrinkage estimators, we establish asymptotic optimality, regret bounds, and valid inference. Unlike existing work, we work with the binomials directly without resorting to Gaussian approximations. This allows us to work with small sample sizes and/or mean parameters in both one-sample and two-sample settings. We demonstrate our approach using three datasets on firm discrimination, education outcomes, and innovation rates.

Although machine learning tasks are highly sensitive to the quality of input data, relevant datasets can often be challenging for firms to acquire, especially when held privately by a variety of owners. For instance, if these owners are competitors in a downstream market, they may be reluctant to share information. Focusing on supervised learning for regression tasks, we develop a regression market to provide a monetary incentive for data sharing. Our mechanism adopts a Bayesian framework, allowing us to consider a more general class of regression tasks. We present a thorough exploration of the market properties, and show that similar proposals in literature expose the market agents to sizeable financial risks, which can be mitigated in our setup.

The answers to many economic questions depend on the slope and curvature of demand. Estimating demand for differentiated products entails a trade-off between flexibility and scalability. Existing nonparametric approaches face a curse of dimensionality in the number of products. I develop a scalable nonparametric approach using market-level data that overcomes this curse through economically motivated restrictions embedded in many standard models. Simulations and an application to the U.S. beer market demonstrate flexibility in demand slope and curvature, with consequential differences in counterfactual price responses. Estimation in the application takes seconds, versus several hours for a random coefficient nested logit model.

Machine Learning models in finance are highly susceptible to model drift, where predictive performance declines as data distributions shift. This issue is especially acute in developing economies such as those in Central Asia and the Caucasus - including Tajikistan, Uzbekistan, Kazakhstan, and Azerbaijan - where frequent and unpredictable macroeconomics shocks destabilize financial data. To the best of our knowledge, this is among the first studies to examine drift mitigation methods on financial datasets from these regions. We investigate the use of synthetic outliers, a largely unexplored approach, to improve model stability against unforeseen shocks. To evaluate effectiveness, we introduce a two-level framework that measures both the extent of performance degradation and the severity of shocks. Our experiments on macroeconomic tabular datasets show that adding a small proportion of synthetic outliers generally improves stability compared to baseline models, though the optimal amount varies by dataset and model

This study examines the effects of de-globalization trends on international trade networks and their role in improving forecasts for economic growth. Using section-level trade data from nearly 200 countries from 2010 to 2022, we identify significant shifts in the network topology driven by rising trade policy uncertainty. Our analysis highlights key global players through centrality rankings, with the United States, China, and Germany maintaining consistent dominance. Using a horse race of supervised regressors, we find that network topology descriptors evaluated from section-specific trade networks substantially enhance the quality of a country's GDP growth forecast. We also find that non-linear models, such as Random Forest, XGBoost, and LightGBM, outperform traditional linear models used in the economics literature. Using SHAP values to interpret these non-linear model's predictions, we find that about half of most important features originate from the network descriptors, underscoring their vital role in refining forecasts. Moreover, this study emphasizes the significance of recent economic performance, population growth, and the primary sector's influence in shaping economic growth predictions, offering novel insights into the intricacies of economic growth forecasting.

The intricate dynamics of stock markets have led to extensive research on models that are able to effectively explain their inherent complexities. This study leverages the econometrics literature to explore the dynamic factor model as an interpretable model with sufficient predictive capabilities for capturing essential market phenomena. Although the model has been extensively applied for predictive purposes, this study focuses on analyzing the extracted loadings and common factors as an alternative framework for understanding stock price dynamics. The results reveal novel insights into traditional market theories when applied to the Philippine Stock Exchange using the Kalman method and maximum likelihood estimation, with subsequent validation against the capital asset pricing model. Notably, a one-factor model extracts a common factor representing systematic or market dynamics similar to the composite index, whereas a two-factor model extracts common factors representing market trends and volatility. Furthermore, an application of the model for nowcasting the growth rates of the Philippine gross domestic product highlights the potential of the extracted common factors as viable real-time market indicators, yielding over a 34% decrease in the out-of-sample prediction error. Overall, the results underscore the value of dynamic factor analysis in gaining a deeper understanding of market price movement dynamics.

Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are discrete. In this paper we find that classical estimators, including the maximum score estimator, (Manski (1975)), loose their attractive statistical properties without point identification. First of all, they are not sharp with the estimator converging to an outer region of the identified set, (Komarova (2013)), and in many discrete designs it weakly converges to a random set. Second, they are not robust, with their distribution limit discontinuously changing with respect to the parameters of the model. We propose a novel class of estimators based on the concept of a quantile of a random set, which we show to be both sharp and robust. We demonstrate that our approach extends from cross-sectional settings to classical static and dynamic discrete panel data models.

This study explores the integration of large language models (LLMs) into classic inflation nowcasting frameworks, particularly in light of high inflation volatility periods such as the COVID-19 pandemic. We propose InflaBERT, a BERT-based LLM fine-tuned to predict inflation-related sentiment in news. We use this model to produce NEWS, an index capturing the monthly sentiment of the news regarding inflation. Incorporating our expectation index into the Cleveland Fed's model, which is only based on macroeconomic autoregressive processes, shows a marginal improvement in nowcast accuracy during the pandemic. This highlights the potential of combining sentiment analysis with traditional economic indicators, suggesting further research to refine these methodologies for better real-time inflation monitoring. The source code is available at https://github.com/paultltc/InflaBERT.

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.

Classical estimators for ARIMA parameters (MLE, CSS, OLS) assume Gaussian innovations, an assumption frequently violated in financial and economic data exhibiting asymmetric distributions with heavy tails. We develop and validate the second-order polynomial maximization method (PMM2) for estimating ARIMA(p,d,q) models with non-Gaussian innovations. PMM2 is a semiparametric technique that exploits higher-order moments and cumulants without requiring full distributional specification. Monte Carlo experiments (128,000 simulations) across sample sizes N in {100, 200, 500, 1000} and four innovation distributions demonstrate that PMM2 substantially outperforms classical methods for asymmetric innovations. For ARIMA(1,1,0) with N=500, relative efficiency reaches 1.58--1.90 for Gamma, lognormal, and χ^2(3) innovations (37--47\% variance reduction). Under Gaussian innovations PMM2 matches OLS efficiency, avoiding the precision loss typical of robust estimators. The method delivers major gains for moderate asymmetry (|γ_3| geq 0.5) and N geq 200, with computational costs comparable to MLE. PMM2 provides an effective alternative for time series with asymmetric innovations typical of financial markets, macroeconomic indicators, and industrial measurements. Future extensions include seasonal SARIMA models, GARCH integration, and automatic order selection.

This paper evaluates the performance of prominent machine learning (ML) algorithms in predicting Indonesia's inflation using the payment system, capital market, and macroeconomic data. We compare the forecasting performance of each ML model, namely shrinkage regression, ensemble learning, and super vector regression, to that of the univariate time series ARIMA and SARIMA models. We examine various out-of-bag sample periods in each ML model to determine the appropriate data-splitting ratios for the regression case study. This study indicates that all ML models produced lower RMSEs and reduced average forecast errors by 45.16 percent relative to the ARIMA benchmark, with the Extreme Gradient Boosting model outperforming other ML models and the benchmark. Using the Shapley value, we discovered that numerous payment system variables significantly predict inflation. We explore the ML forecast using local Shapley decomposition and show the relationship between the explanatory variables and inflation for interpretation. The interpretation of the ML forecast highlights some significant findings and offers insightful recommendations, enhancing previous economic research that uses a more established econometric method. Our findings advocate ML models as supplementary tools for the central bank to predict inflation and support monetary policy.

Time series analysis and forecasting of stock market prices has been a very active area of research over the last two decades. Availability of extremely fast and parallel architecture of computing and sophisticated algorithms has made it possible to extract, store, process and analyze high volume stock market time series data very efficiently. In this paper, we have used time series data of the two sectors of the Indian economy: Information Technology and Capital Goods for the period January 2009 till April 2016 and have studied the relationships of these two time series with the time series of DJIA index, NIFTY index and the US Dollar to Indian Rupee exchange rate. We establish by graphical and statistical tests that while the IT sector of India has a strong association with DJIA index and the Dollar to Rupee exchange rate, the Indian CG sector exhibits a strong association with the NIFTY index. We contend that these observations corroborate our hypotheses that the Indian IT sector is strongly coupled with the world economy whereas the CG sector of India reflects internal economic growth of India. We also present several models of regression between the time series which exhibit strong association among them. The effectiveness of these models have been demonstrated by very low values of their forecasting errors.

Researchers are usually interested in examining the impact of covariates when separating heterogeneous samples into latent classes that are more homogeneous. The majority of theoretical and empirical studies with such aims have focused on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, the covariates only indirectly affect the sample heterogeneity. However, the covariates' influence on between-individual differences can also be direct. This article presents a mixture model that investigates covariates to explain within-cluster and between-cluster heterogeneity simultaneously, known as a mixture-of-experts (MoE) model. This study aims to extend the MoE framework to investigate heterogeneity in nonlinear trajectories: to identify latent classes, covariates as predictors to clusters, and covariates that explain within-cluster differences in change patterns over time. Our simulation studies demonstrate that the proposed model generally estimates the parameters unbiasedly, precisely and exhibits appropriate empirical coverage for a nominal 95% confidence interval. This study also proposes implementing structural equation model forests to shrink the covariate space of the proposed mixture model. We illustrate how to select covariates and construct the proposed model with longitudinal mathematics achievement data. Additionally, we demonstrate that the proposed mixture model can be further extended in the structural equation modeling framework by allowing the covariates that have direct effects to be time-varying.

This paper presents a Bayesian nonparametric latent feature model specially suitable for exploratory analysis of high-dimensional count data. We perform a non-negative doubly sparse matrix factorization that has two main advantages: not only we are able to better approximate the row input distributions, but the inferred topics are also easier to interpret. By combining the three-parameter and restricted Indian buffet processes into a single prior, we increase the model flexibility, allowing for a full spectrum of sparse solutions in the latent space. We demonstrate the usefulness of our approach in the analysis of countries' economic structure. Compared to other approaches, empirical results show our model's ability to give easy-to-interpret information and better capture the underlying sparsity structure of data.

In this paper we construct an inferential procedure for Granger causality in high-dimensional non-stationary vector autoregressive (VAR) models. Our method does not require knowledge of the order of integration of the time series under consideration. We augment the VAR with at least as many lags as the suspected maximum order of integration, an approach which has been proven to be robust against the presence of unit roots in low dimensions. We prove that we can restrict the augmentation to only the variables of interest for the testing, thereby making the approach suitable for high dimensions. We combine this lag augmentation with a post-double-selection procedure in which a set of initial penalized regressions is performed to select the relevant variables for both the Granger causing and caused variables. We then establish uniform asymptotic normality of a second-stage regression involving only the selected variables. Finite sample simulations show good performance, an application to investigate the (predictive) causes and effects of economic uncertainty illustrates the need to allow for unknown orders of integration.

Volatility clustering is an important characteristic that has a significant effect on the behavior of stock markets. However, designing robust models for accurate prediction of future volatilities of stock prices is a very challenging research problem. We present several volatility models based on generalized autoregressive conditional heteroscedasticity (GARCH) framework for modeling the volatility of ten stocks listed in the national stock exchange (NSE) of India. The stocks are selected from the auto sector and the banking sector of the Indian economy, and they have a significant impact on the sectoral index of their respective sectors in the NSE. The historical stock price records from Jan 1, 2010, to Apr 30, 2021, are scraped from the Yahoo Finance website using the DataReader API of the Pandas module in the Python programming language. The GARCH modules are built and fine-tuned on the training data and then tested on the out-of-sample data to evaluate the performance of the models. The analysis of the results shows that asymmetric GARCH models yield more accurate forecasts on the future volatility of stocks.

Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding process may be ill-suited to continuous-valued outputs, where obtaining predictive distributions over numerical targets requires repeated sampling, leading to high computational cost and inference time. In this work, we investigate whether distributional properties of LLM predictions can be recovered without explicit autoregressive generation. To this end, we study a set of regression probes trained to predict statistical functionals (e.g., mean, median, quantiles) of the LLM's numerical output distribution directly from its internal representations. Our results suggest that LLM embeddings carry informative signals about summary statistics of their predictive distributions, including the numerical uncertainty. This investigation opens up new questions about how LLMs internally encode uncertainty in numerical tasks, and about the feasibility of lightweight alternatives to sampling-based approaches for uncertainty-aware numerical predictions.

We present t_0, a family of open-weights foundation models for forecasting with multivariate context. We release its first two members: t0-alpha and t0-beta, respectively 102M and 256M parameters. Both condition their forecasts on target history, past covariates, and known-future covariates, without task-specific retraining. Their transformer layers alternate attention along time and across variates. They produce probabilistic forecasts through quantile predictions. Pretraining combines curated public data with synthetic generator families constructed to contain covariate-to-target dependencies. On GIFT-Eval, t0-alpha reaches an aggregate CRPS of 0.4941, and t0-beta a CRPS of 0.4738 and a MASE of 0.6865, third on both and within 4.0% of the best zero-shot TSFM. On fev-bench they score 42.2 and 46.7 in skill, the latter third again and 2.0 points behind the leader. We analyze t0-alpha in depth. Known-future covariates raise its skill by 6.3 percentage points across 30 tasks. The report also examines its calibration, its rollout strategy on long horizons, and its robustness to missing data. On the Victoria electricity-demand benchmark, t0-beta is among the most accurate models with a context of nearly a year. In an independent Macrocosm evaluation of hourly ERCOT prices over 29 months, both cut the MAE of the lagged-price baseline by 38%.

Can AI effectively perform complex econometric analysis traditionally requiring human expertise? This paper evaluates an agentic AI's capability to master econometrics, focusing on empirical analysis performance. We develop an ``Econometrics AI Agent'' built on the open-source MetaGPT framework. This agent exhibits outstanding performance in: (1) planning econometric tasks strategically, (2) generating and executing code, (3) employing error-based reflection for improved robustness, and (4) allowing iterative refinement through multi-round conversations. We construct two datasets from academic coursework materials and published research papers to evaluate performance against real-world challenges. Comparative testing shows our domain-specialized agent significantly outperforms both benchmark large language models (LLMs) and general-purpose AI agents. This work establishes a testbed for exploring AI's impact on social science research and enables cost-effective integration of domain expertise, making advanced econometric methods accessible to users with minimal coding expertise. Furthermore, our agent enhances research reproducibility and offers promising pedagogical applications for econometrics teaching.

Autoregressive foundation models offer state-of-the-art capabilities to simulate the market by generating the message flow of limit order books (LOBs). Yet, without understanding their inner workings, research directions are hard to narrow and practical use in real-world trading environments remains uncertain. This study therefore asks what these models actually learn about market microstructure. We find that, similarly to games where sequence models build an internal representation of the board, an 8.2M-parameter Mamba-3 state-space model trained autoregressively on the tokenized message stream of eight large-cap US equities learns an internal representation of the market and its dynamics. In particular, order-flow imbalance, a central driver of short-horizon price moves, is decodable at R^2 approx 0.59, far above controls and baselines. This representation extends to unseen stocks, suggesting that these models learn general representations rather than ticker-specific patterns. The model also generalizes across metrics beyond order-flow imbalance: results hold across traded volume and volatility. Additionally, the representation is causally steerable: pushing the state along a feature's axis shifts the model's next-message beliefs as that feature implies, monotonically in dose, consistent with the emergence of a world model.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

The rapid development of large language models (LLMs) has renewed interest in agent-based modeling (ABM). However, current LLM-based ABM research faces several key challenges: modeling evolving agent-environment interactions, enabling flexible counterfactual reasoning, and automating simulation workflows for scientific research. In this paper, we propose Eco3S, a socio-economic system simulation framework for economic research and policy analysis that addresses these challenges through three key mechanisms: (1) Co-evolving Environment Design, a bidirectional feedback loop where agents and the environment co-evolve, producing realistic emergent behaviors; (2) Structural Causal Simulation, a structural causal model (SCM)-inspired counterfactual mechanism that allows flexible interventions for diverse causal inference tasks; (3) Simulation-Analysis-Refinement Paradigm, a self-corrective mechanism that iteratively refines experimental designs based on prior simulation results. Experiments on diverse economic scenarios confirm Eco3S's effectiveness in replicating multiple established economic studies (canal decay, origins of governance, and information propagation) and phenomena across domains. Additional results further demonstrate its scalability and generalizability, highlighting the framework's potential for rigorous economic research and policy-making.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Multilevel data are prevalent in many real-world applications. However, it remains an open research problem to identify and justify a class of models that flexibly capture a wide range of multilevel data. Motivated by the versatility of the mixture of experts (MoE) models in fitting regression data, in this article we extend upon the MoE and study a class of mixed MoE (MMoE) models for multilevel data. Under some regularity conditions, we prove that the MMoE is dense in the space of any continuous mixed effects models in the sense of weak convergence. As a result, the MMoE has a potential to accurately resemble almost all characteristics inherited in multilevel data, including the marginal distributions, dependence structures, regression links, random intercepts and random slopes. In a particular case where the multilevel data is hierarchical, we further show that a nested version of the MMoE universally approximates a broad range of dependence structures of the random effects among different factor levels.

A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional game has been a source of controversy. The two main approaches that have been proposed differ in the way that they condition on known features, using either (1) an interventional or (2) an observational conditional expectation. While previous work has argued that one of the two approaches is preferable in general, we argue that the choice is application dependent. Furthermore, we argue that the choice comes down to whether it is desirable to be true to the model or true to the data. We use linear models to investigate this choice. After deriving an efficient method for calculating observational conditional expectation Shapley values for linear models, we investigate how correlation in simulated data impacts the convergence of observational conditional expectation Shapley values. Finally, we present two real data examples that we consider to be representative of possible use cases for feature attribution -- (1) credit risk modeling and (2) biological discovery. We show how a different choice of value function performs better in each scenario, and how possible attributions are impacted by modeling choices.

This article presents Individual Conditional Expectation (ICE) plots, a tool for visualizing the model estimated by any supervised learning algorithm. Classical partial dependence plots (PDPs) help visualize the average partial relationship between the predicted response and one or more features. In the presence of substantial interaction effects, the partial response relationship can be heterogeneous. Thus, an average curve, such as the PDP, can obfuscate the complexity of the modeled relationship. Accordingly, ICE plots refine the partial dependence plot by graphing the functional relationship between the predicted response and the feature for individual observations. Specifically, ICE plots highlight the variation in the fitted values across the range of a covariate, suggesting where and to what extent heterogeneities might exist. In addition to providing a plotting suite for exploratory analysis, we include a visual test for additive structure in the data generating model. Through simulated examples and real data sets, we demonstrate how ICE plots can shed light on estimated models in ways PDPs cannot. Procedures outlined are available in the R package ICEbox.

Organizations typically train large models individually. This is costly and time-consuming, particularly for large-scale foundation models. Such vertical production is known to be suboptimal. Inspired by this economic insight, we ask whether it is possible to leverage others' expertise by trading the constituent parts in models, i.e., sets of weights, as if they were market commodities. While recent advances in aligning and interpolating models suggest that doing so may be possible, a number of fundamental questions must be answered to create viable parameter markets. In this work, we address these basic questions, propose a framework containing the infrastructure necessary for market operations to take place, study strategies for exchanging parameters, and offer means for agents to monetize parameters. Excitingly, compared to agents who train siloed models from scratch, we show that it is possible to mutually gain by using the market, even in competitive settings. This suggests that the notion of parameter markets may be a useful paradigm for improving large-scale model training in the future.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Large Language Models (LLMs) show significant potential in economic and strategic interactions, where communication via natural language is often prevalent. This raises key questions: Do LLMs behave rationally? Can they mimic human behavior? Do they tend to reach an efficient and fair outcome? What is the role of natural language in the strategic interaction? How do characteristics of the economic environment influence these dynamics? These questions become crucial concerning the economic and societal implications of integrating LLM-based agents into real-world data-driven systems, such as online retail platforms and recommender systems. While the ML community has been exploring the potential of LLMs in such multi-agent setups, varying assumptions, design choices and evaluation criteria across studies make it difficult to draw robust and meaningful conclusions. To address this, we introduce a benchmark for standardizing research on two-player, sequential, language-based games. Inspired by the economic literature, we define three base families of games with consistent parameterization, degrees of freedom and economic measures to evaluate agents' performance (self-gain), as well as the game outcome (efficiency and fairness). We develop an open-source framework for interaction simulation and analysis, and utilize it to collect a dataset of LLM vs. LLM interactions across numerous game configurations and an additional dataset of human vs. LLM interactions. Through extensive experimentation, we demonstrate how our framework and dataset can be used to: (i) compare the behavior of LLM-based agents to human players in various economic contexts; (ii) evaluate agents in both individual and collective performance measures; and (iii) quantify the effect of the economic characteristics of the environments on the behavior of agents.

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient online 2SLS and the efficient SGMM. Moreover, we propose online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be seamlessly integrated within the SGMM framework. Extensive Monte Carlo simulations show that as the sample size increases, the SGMM matches the standard (offline) GMM in terms of estimation accuracy and gains over computational efficiency, indicating its practical value for both large-scale and online datasets. We demonstrate the efficacy of our approach by a proof of concept using two well known empirical examples with large sample sizes.

Large language models (LLMs) have the potential to meet a key goal in economics: a quantitative model of household decision making, across a variety of settings. Yet existing evaluations cover few surveys and outcomes, and do not study how households adjust to changing economic conditions. We introduce a new evaluation, HouseholdBench, which unites 6 U.S. household surveys and 32 prediction tasks spanning numeric, categorical and probabilistic outcomes, related to consumption, income, labor, expectations, and housing. Using past behavior, demographics and macroeconomic conditions, the tasks test whether LLMs predict behavior, including how households adjust to changes in various policies. We evaluate 13 proprietary and open-weight LLMs against a no-change baseline and a gradient-boosted tree model. Most LLMs outperform the no-change baseline, including for policy response tasks -- with the best model lowering error for numeric outcomes by 12.2%. Across most tasks, gradient-boosted trees rank first; leading proprietary LLMs approach their performance, but open-weight models lag. LLMs exhibit systematic over- and underprediction across different tasks. We identify methods that enable a 4 billion parameter open-weight model to match proprietary models' performance: fine-tuning and aggregating 16 predictions per observation. Improvements generalize to policy-response tasks, which are excluded from fine-tuning. We release our datasets, code, and leaderboard on our website: https://jn-huang.github.io/householdbench

In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. Agents are assumed to have three components to the expectation of future asset returns, namely-fundamentalist, chartist and noise trader. Furthermore agents differ in the characteristics describing these components, such as time horizon, risk aversion and the weights given to the various components. The model developed here extends a great deal of earlier literature in that the order submissions of agents are determined by utility maximisation, rather than the mechanical unit order size that is commonly assumed. In this way the order flow is better related to the ongoing evolution of the market. For the given market structure we analyze the impact of the three components of the trading strategies on the statistical properties of prices and order flows and observe that it is the chartist strategy that is mainly responsible of the fat tails and clustering in the artificial price data generated by the model. The paper provides further evidence that large price changes are likely to be generated by the presence of large gaps in the book.

Diffusion models, initially developed for image synthesis, demonstrate remarkable generative capabilities. Recently, their application has expanded to time series forecasting (TSF), yielding promising results. Existing surveys on time series primarily focus on the application of diffusion models to time series tasks or merely provide model-by-model introductions of diffusion-based TSF models, without establishing a systematic taxonomy for existing diffusion-based TSF models. In this survey, we firstly introduce several standard diffusion models and their prevalent variants, explaining their adaptation to TSF tasks. Then, we provide a comprehensive review of diffusion models for TSF, paying special attention to the sources of conditional information and the mechanisms for integrating this conditioning within the models. In analyzing existing approaches using diffusion models for TSF, we provide a systematic categorization and a comprehensive summary of them in this survey. Furthermore, we examine several foundational diffusion models applied to TSF, alongside commonly used datasets and evaluation metrics. Finally, we discuss the progress and limitations of these approaches, as well as potential future research directions for diffusion-based TSF. Overall, this survey offers a comprehensive overview of recent progress and future prospects for diffusion models in TSF, serving as a valuable reference for researchers in the field.

This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used throughout the book and serve at a reminder of basic concepts in calculus, linear algebra and probability and also introduces some measure theoretic terminology, which can be used as a reading guide for the sections that use these tools. The introductory chapters also provide background material on matrix analysis and optimization. The latter chapter provides theoretical support to many algorithms that are used in the book, including stochastic gradient descent, proximal methods, etc. After discussing basic concepts for statistical prediction, the book includes an introduction to reproducing kernel theory and Hilbert space techniques, which are used in many places, before addressing the description of various algorithms for supervised statistical learning, including linear methods, support vector machines, decision trees, boosting, or neural networks. The subject then switches to generative methods, starting with a chapter that presents sampling methods and an introduction to the theory of Markov chains. The following chapter describe the theory of graphical models, an introduction to variational methods for models with latent variables, and to deep-learning based generative models. The next chapters focus on unsupervised learning methods, for clustering, factor analysis and manifold learning. The final chapter of the book is theory-oriented and discusses concentration inequalities and generalization bounds.

We present a new estimator for causal effects with panel data that builds on insights behind the widely used difference in differences and synthetic control methods. Relative to these methods we find, both theoretically and empirically, that this "synthetic difference in differences" estimator has desirable robustness properties, and that it performs well in settings where the conventional estimators are commonly used in practice. We study the asymptotic behavior of the estimator when the systematic part of the outcome model includes latent unit factors interacted with latent time factors, and we present conditions for consistency and asymptotic normality.

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models are either designed for unweighted graphs and are not easily extended to weighted topologies or incorporate edge weights without consideration of a joint distribution with topology. Furthermore, learning a distribution over weighted graphs must account for complex nonlocal dependencies between both the edges of the graph and corresponding weights of each edge. We develop an autoregressive model BiGG-E, a nontrivial extension of the BiGG model, that learns a joint distribution over weighted graphs while still exploiting sparsity to generate a weighted graph with n nodes and m edges in O((n + m)log n) time. Simulation studies and experiments on a variety of benchmark datasets demonstrate that BiGG-E best captures distributions over weighted graphs while remaining scalable and computationally efficient.

Autoregressive models (ARMs) currently constitute the dominant paradigm for large language models (LLMs). Energy-based models (EBMs) represent another class of models, which have historically been less prevalent in LLM development, yet naturally characterize the optimal policy in post-training alignment. In this paper, we provide a unified view of these two model classes. Taking the chain rule of probability as a starting point, we establish an explicit bijection between ARMs and EBMs in function space, which we show to correspond to a special case of the soft Bellman equation in maximum entropy reinforcement learning. Building upon this bijection, we derive the equivalence between supervised learning of ARMs and EBMs. Furthermore, we analyze the distillation of EBMs into ARMs by providing theoretical error bounds. Our results provide insights into the ability of ARMs to plan ahead, despite being based on the next-token prediction paradigm.

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.

Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a varphi-divergence to an empirical distribution. However, the use of varphi-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

Longitudinal observational data are often subject to informative missingness. For example, in healthcare research using electronic health records, covariates and outcomes are measured only when patients interact with the healthcare system. Whether these data are observed usually depends on the unobserved variable values themselves, introducing a common form of data missing not at random. We develop identification and estimation methods for the effects of longitudinal modified treatment policies under a self-censoring model which explicitly models this dependence. We consider effects of treatments that can be modified only at measurement times (e.g., interactions with the heathcare system). We study two settings: one in which the observed history suffices for treatment confounding control, and another in which confounder control requires covariate values that were not measured at missed visits. In both settings, we combine longitudinal causal identification with shadow-variable conditional moment restrictions to obtain recursive identification formulas for the counterfactual outcome mean. We derive gradients of the pathwise derivatives and second-order remainder expansions, and use these results to construct estimators that accommodate machine learning for nuisance-function estimation. Under suitable product-rate conditions and cross-fitting, the estimators are asymptotically linear and permit root-n inference, including simultaneous inference across outcome times. We also describe conditional-moment learning and ensemble approaches for estimating the nuisance functions required by our approach, together with a pool-and-smooth strategy that borrows information across sparsely measured outcomes.

Time series analysis has witnessed the inspiring development from traditional autoregressive models, deep learning models, to recent Transformers and Large Language Models (LLMs). Efforts in leveraging vision models for time series analysis have also been made along the way but are less visible to the community due to the predominant research on sequence modeling in this domain. However, the discrepancy between continuous time series and the discrete token space of LLMs, and the challenges in explicitly modeling the correlations of variates in multivariate time series have shifted some research attentions to the equally successful Large Vision Models (LVMs) and Vision Language Models (VLMs). To fill the blank in the existing literature, this survey discusses the advantages of vision models over LLMs in time series analysis. It provides a comprehensive and in-depth overview of the existing methods, with dual views of detailed taxonomy that answer the key research questions including how to encode time series as images and how to model the imaged time series for various tasks. Additionally, we address the challenges in the pre- and post-processing steps involved in this framework and outline future directions to further advance time series analysis with vision models.

This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies generation and forecasting, and provides hyperparameter estimates, which we exploit in a convergent and consistent iterative estimation algorithm. A bootstrap approach for standard error estimation and confidence intervals is also provided. We demonstrate the computational and scaling benefits of the proposed approach on a broad class of problems, including water level tidal analysis, CO_{2} emission data, and sunspot numbers data. By leveraging the structural equations, our method reduces the cost of likelihood evaluations and predictions from O(k^2 p^2) to O(p^2), significantly improving scalability.

This study examines the relationship between income inequality, gender, and school completion rates in Malaysia using machine learning techniques. The dataset utilized is from the Malaysia's Public Sector Open Data Portal, covering the period 2016-2022. The analysis employs various machine learning techniques, including K-means clustering, ARIMA modeling, Random Forest regression, and Prophet for time series forecasting. These models are used to identify patterns, trends, and anomalies in the data, and to predict future school completion rates. Key findings reveal significant disparities in school completion rates across states, genders, and income levels. The analysis also identifies clusters of states with similar completion rates, suggesting potential regional factors influencing educational outcomes. Furthermore, time series forecasting models accurately predict future completion rates, highlighting the importance of ongoing monitoring and intervention strategies. The study concludes with recommendations for policymakers and educators to address the observed disparities and improve school completion rates in Malaysia. These recommendations include targeted interventions for specific states and demographic groups, investment in early childhood education, and addressing the impact of income inequality on educational opportunities. The findings of this study contribute to the understanding of the factors influencing school completion in Malaysia and provide valuable insights for policymakers and educators to develop effective strategies to improve educational outcomes.

The GDP of a country is modelled as the relative interaction between two agents - working hours, reflecting the social choice of a population, and Total Factor Productivity, reflecting the collective investment in productivity enhancers. It is shown that a Random Forest model can accu- rately predict the GDP from these two factors. The differences in the choices made by Germany and USA are analysed though Gini importance, SHAP plots and partial dependency. It is shown that the differences in the social structure of the countries are reflected in the relative contribution of working hours and productivity to the GDP.

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semi-parametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the o_p(n^{-1/4}) rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

We propose a general methodology for recovering preference parameters from data on choices and response times. Our methods yield estimates with fast (1/n for n data points) convergence rates when specialized to the popular Drift Diffusion Model (DDM), but are broadly applicable to generalizations of the DDM as well as to alternative models of decision making that make use of response time data. The paper develops an empirical application to an experiment on intertemporal choice, showing that the use of response times delivers predictive accuracy and matters for the estimation of economically relevant parameters.

How should one judge whether a given large language model (LLM) can reliably perform economic reasoning? Most existing LLM benchmarks focus on specific applications and fail to present the model with a rich variety of economic tasks. A notable exception is Raman et al. [2024], who offer an approach for comprehensively benchmarking strategic decision-making; however, this approach fails to address the non-strategic settings prevalent in microeconomics, such as supply-and-demand analysis. We address this gap by taxonomizing microeconomic reasoning into 58 distinct elements, focusing on the logic of supply and demand, each grounded in up to 10 distinct domains, 5 perspectives, and 3 types. The generation of benchmark data across this combinatorial space is powered by a novel LLM-assisted data generation protocol that we dub auto-STEER, which generates a set of questions by adapting handwritten templates to target new domains and perspectives. Because it offers an automated way of generating fresh questions, auto-STEER mitigates the risk that LLMs will be trained to over-fit evaluation benchmarks; we thus hope that it will serve as a useful tool both for evaluating and fine-tuning models for years to come. We demonstrate the usefulness of our benchmark via a case study on 27 LLMs, ranging from small open-source models to the current state of the art. We examined each model's ability to solve microeconomic problems across our whole taxonomy and present the results across a range of prompting strategies and scoring metrics.

This study analyzes Sri Lankan migration and remittances over 32 years (1994-2025). Using a 384-month harmonized dataset, we apply exploratory data analysis, stationarity corrected time-series modeling (ADF, Johansen, VAR/VECM), and supervised learning. Results reveal remittance inflows are primarily driven by external macroeconomic variables, specifically exchange rate dynamics and global oil prices, rather than domestic indicators. Impulse response analysis confirms the asymmetric impact of currency depreciation and oil price shocks. Predictively, multivariate machine learning models outperform traditional univariate approaches; Ridge Regression achieves a 73.8% accuracy improvement over SARIMA (Annualized RMSE: USD 494.8 Mn). The optimized framework projects 2026 remittances at USD 9,001 million under stable conditions. These findings highlight the structural dependence of remittances on global economies, emphasizing the need for robust exchange rate policies, skilled migration, and formal financial channels to enhance long-term economic resilience.

Vegetable prices in Sri Lanka are highly volatile because the market is largely import-isolated, so supply disruptions quickly drive prices up. This study develops a machine learning framework to forecast such volatility by incorporating supply-chain-aware features and explicitly modelling the country's two cultivation seasons, Maha (October-April) and Yala (May-September). An integrated dataset was constructed by combining retail and farmer-gate prices with origin-aligned weather variables, diesel costs, and exchange rates across 12 vegetable varieties and 14 market centres from 2013 to 2019. A gradient-boosted ensemble model (XGBoost and LightGBM) was trained and optimised using Optuna, and unified and season-specific configurations were compared. Results show that season-specific models improve within-season fit, with the Yala-specific model achieving the highest R2 of 0.9420 (95% CI [0.690, 1.000]), while the unified model delivers the best overall predictive accuracy of 90.84% (95% CI [88.34%, 91.52%]) and an R2 of 0.9281 (95% CI [0.760, 1.000]). Notably, the unified model maintains 85.96% accuracy on a completely unseen 2024 hyperinflationary period without retraining, successfully tracking major price surges. These findings suggest that agricultural price movements in import-constrained markets are meaningfully predictable when models capture supply-chain dynamics, offering practical value for early warning and decision making by farmers, traders, and policymakers. Existing studies on Sri Lankan vegetable prices are confined to Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) applied to single markets, with no supply-chain features, seasonal segmentation, or cross-regime validation.

When solving forecasting problems including multiple time-series features, existing approaches often fall into two extreme categories, depending on whether to utilize inter-feature information: univariate and complete-multivariate models. Unlike univariate cases which ignore the information, complete-multivariate models compute relationships among a complete set of features. However, despite the potential advantage of leveraging the additional information, complete-multivariate models sometimes underperform univariate ones. Therefore, our research aims to explore a middle ground between these two by introducing what we term Partial-Multivariate models where a neural network captures only partial relationships, that is, dependencies within subsets of all features. To this end, we propose PMformer, a Transformer-based partial-multivariate model, with its training algorithm. We demonstrate that PMformer outperforms various univariate and complete-multivariate models, providing a theoretical rationale and empirical analysis for its superiority. Additionally, by proposing an inference technique for PMformer, the forecasting accuracy is further enhanced. Finally, we highlight other advantages of PMformer: efficiency and robustness under missing features.

Causal effects are usually studied in terms of the means of counterfactual distributions, which may be insufficient in many scenarios. Given a class of densities known up to normalizing constants, we propose to model counterfactual distributions by minimizing kernel Stein discrepancies in a doubly robust manner. This enables the estimation of counterfactuals over large classes of distributions while exploiting the desired double robustness. We present a theoretical analysis of the proposed estimator, providing sufficient conditions for consistency and asymptotic normality, as well as an examination of its empirical performance.

Autoregressive modeling has been a huge success in the field of natural language processing (NLP). Recently, autoregressive models have emerged as a significant area of focus in computer vision, where they excel in producing high-quality visual content. Autoregressive models in NLP typically operate on subword tokens. However, the representation strategy in computer vision can vary in different levels, i.e., pixel-level, token-level, or scale-level, reflecting the diverse and hierarchical nature of visual data compared to the sequential structure of language. This survey comprehensively examines the literature on autoregressive models applied to vision. To improve readability for researchers from diverse research backgrounds, we start with preliminary sequence representation and modeling in vision. Next, we divide the fundamental frameworks of visual autoregressive models into three general sub-categories, including pixel-based, token-based, and scale-based models based on the strategy of representation. We then explore the interconnections between autoregressive models and other generative models. Furthermore, we present a multi-faceted categorization of autoregressive models in computer vision, including image generation, video generation, 3D generation, and multi-modal generation. We also elaborate on their applications in diverse domains, including emerging domains such as embodied AI and 3D medical AI, with about 250 related references. Finally, we highlight the current challenges to autoregressive models in vision with suggestions about potential research directions. We have also set up a Github repository to organize the papers included in this survey at: https://github.com/ChaofanTao/Autoregressive-Models-in-Vision-Survey.

Is bigger always better for time series foundation models? With the question in mind, we explore an alternative to training a single, large monolithic model: building a portfolio of smaller, pretrained forecasting models. By applying ensembling or model selection over these portfolios, we achieve competitive performance on large-scale benchmarks using much fewer parameters. We explore strategies for designing such portfolios and find that collections of specialist models consistently outperform portfolios of independently trained generalists. Remarkably, we demonstrate that post-training a base model is a compute-effective approach for creating sufficiently diverse specialists, and provide evidences that ensembling and model selection are more compute-efficient than test-time fine-tuning.

Building predictive models for robust and accurate prediction of stock prices and stock price movement is a challenging research problem to solve. The well-known efficient market hypothesis believes in the impossibility of accurate prediction of future stock prices in an efficient stock market as the stock prices are assumed to be purely stochastic. However, numerous works proposed by researchers have demonstrated that it is possible to predict future stock prices with a high level of precision using sophisticated algorithms, model architectures, and the selection of appropriate variables in the models. This chapter proposes a collection of predictive regression models built on deep learning architecture for robust and precise prediction of the future prices of a stock listed in the diversified sectors in the National Stock Exchange (NSE) of India. The Metastock tool is used to download the historical stock prices over a period of two years (2013- 2014) at 5 minutes intervals. While the records for the first year are used to train the models, the testing is carried out using the remaining records. The design approaches of all the models and their performance results are presented in detail. The models are also compared based on their execution time and accuracy of prediction.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential importance. Here we propose a maximum-likelihood approach for model analysis in a fully dynamical framework that includes time-ordered experimental data. Our methods can be applied to dynamical models for the prediction of discrete behavior (e.g., movement onsets), in particular, we use a dynamical model of saccade generation in scene viewing as a case study for our approach. For this model, the likelihood function can be computed directly by numerical simulation, which enables more efficient parameter estimation including Bayesian inference to obtain reliable estimates and corresponding credible intervals. Using hierarchical models inference is even possible for individual observers. Furthermore, our likelihood approach can be used to compare different models. In our example, the dynamical framework is shown to outperform non-dynamical statistical models. Additionally, the likelihood based evaluation differentiates model variants, which produced indistinguishable predictions on hitherto used statistics. Our results indicate that the likelihood approach is a promising framework for dynamical cognitive models.

Estimating causal effect using machine learning (ML) algorithms can help to relax functional form assumptions if used within appropriate frameworks. However, most of these frameworks assume settings with cross-sectional data, whereas researchers often have access to panel data, which in traditional methods helps to deal with unobserved heterogeneity between units. In this paper, we explore how we can adapt double/debiased machine learning (DML) (Chernozhukov et al., 2018) for panel data in the presence of unobserved heterogeneity. This adaptation is challenging because DML's cross-fitting procedure assumes independent data and the unobserved heterogeneity is not necessarily additively separable in settings with nonlinear observed confounding. We assess the performance of several intuitively appealing estimators in a variety of simulations. While we find violations of the cross-fitting assumptions to be largely inconsequential for the accuracy of the effect estimates, many of the considered methods fail to adequately account for the presence of unobserved heterogeneity. However, we find that using predictive models based on the correlated random effects approach (Mundlak, 1978) within DML leads to accurate coefficient estimates across settings, given a sample size that is large relative to the number of observed confounders. We also show that the influence of the unobserved heterogeneity on the observed confounders plays a significant role for the performance of most alternative methods.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

Recent work has identified simple empirical scaling laws for language models, linking compute budget, dataset size, model size, and autoregressive modeling loss. The validity of these simple power laws across orders of magnitude in model scale provides compelling evidence that larger models are also more capable models. However, scaling up models under the constraints of hardware and infrastructure is no easy feat, and rapidly becomes a hard and expensive engineering problem. We investigate ways to tentatively cheat scaling laws, and train larger models for cheaper. We emulate an increase in effective parameters, using efficient approximations: either by doping the models with frozen random parameters, or by using fast structured transforms in place of dense linear layers. We find that the scaling relationship between test loss and compute depends only on the actual number of trainable parameters; scaling laws cannot be deceived by spurious parameters.

As large language models increase in capability, researchers have started to conduct surveys of all kinds on these models with varying scientific motivations. In this work, we examine what we can learn from a model's survey responses on the basis of the well-established American Community Survey (ACS) by the U.S. Census Bureau. Evaluating more than a dozen different models, varying in size from a few hundred million to ten billion parameters, hundreds of thousands of times each on questions from the ACS, we systematically establish two dominant patterns. First, smaller models have a significant position and labeling bias, for example, towards survey responses labeled with the letter "A". This A-bias diminishes, albeit slowly, as model size increases. Second, when adjusting for this labeling bias through randomized answer ordering, models still do not trend toward US population statistics or those of any cognizable population. Rather, models across the board trend toward uniformly random aggregate statistics over survey responses. This pattern is robust to various different ways of prompting the model, including what is the de-facto standard. Our findings demonstrate that aggregate statistics of a language model's survey responses lack the signals found in human populations. This absence of statistical signal cautions about the use of survey responses from large language models at present time.

We introduce MACROCAST, a lightweight Time Series Foundation Model (TSFM) for real-time macroeconomic forecasting. Existing TSFMs suffer from data leakage in two forms: temporal contamination, as the model may have seen the realized values of the series it forecasts, and revision bias, as training on fully revised data diverges from the preliminary, vintage-specific releases available to real-time forecasters. MACROCAST is, to our knowledge, the first TSFM that rules out both forms of leakage entirely: at no stage of training is the model exposed to information that would not have been available to a forecaster in real time. We train MACROCAST first on purely synthetic time series in approximately one GPU-day and then fine-tune it on synthetic time series drawn from Bayesian VARs, dynamic factor models, and ARIMA specifications estimated on vintage-specific ALFRED data. Because pretraining uses only simulated data and fine-tuning uses only real-time vintages, no observed future or revised value ever enters the model; each fine-tuning run takes nine minutes. Evaluated on the FRED-MD database in a genuine real-time out-of-sample exercise, MACROCAST improves on the AR(1) benchmark for roughly 80% of series-horizon pairs, matches or surpasses Chronos-2 -- the strongest currently available TSFM -- and outperforms the Bayesian VAR and dynamic factor model benchmarks, all in a data-leakage-free manner.

Integrated autoregressive conditional duration (ACD) models serve as natural counterparts to the well-known integrated GARCH models used for financial returns. However, despite their resemblance, asymptotic theory for ACD is challenging and also not complete, in particular for integrated ACD. Central challenges arise from the facts that (i) integrated ACD processes imply durations with infinite expectation, and (ii) even in the non-integrated case, conventional asymptotic approaches break down due to the randomness in the number of durations within a fixed observation period. Addressing these challenges, we provide here unified asymptotic theory for the (quasi-) maximum likelihood estimator for ACD models; a unified theory which includes integrated ACD models. Based on the new results, we also provide a novel framework for hypothesis testing in duration models, enabling inference on a key empirical question: whether durations possess a finite or infinite expectation. We apply our results to high-frequency cryptocurrency ETF trading data. Motivated by parameter estimates near the integrated ACD boundary, we assess whether durations between trades in these markets have finite expectation, an assumption often made implicitly in the literature on point process models. Our empirical findings indicate infinite-mean durations for all the five cryptocurrencies examined, with the integrated ACD hypothesis rejected -- against alternatives with tail index less than one -- for four out of the five cryptocurrencies considered.

Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model fitting algorithm as a function of the data. However, exchangeability is often violated when predictive models are deployed in practice. For example, if the data distribution drifts over time, then the data points are no longer exchangeable; moreover, in such settings, we might want to use a nonsymmetric algorithm that treats recent observations as more relevant. This paper generalizes conformal prediction to deal with both aspects: we employ weighted quantiles to introduce robustness against distribution drift, and design a new randomization technique to allow for algorithms that do not treat data points symmetrically. Our new methods are provably robust, with substantially less loss of coverage when exchangeability is violated due to distribution drift or other challenging features of real data, while also achieving the same coverage guarantees as existing conformal prediction methods if the data points are in fact exchangeable. We demonstrate the practical utility of these new tools with simulations and real-data experiments on electricity and election forecasting.

We develop a Gaussian comparison theory for posterior inference in non-Gaussian high-dimensional models. The framework allows for model misspecification and does not require the posterior distribution itself to be approximately Gaussian. Working directly with likelihood processes on separable function spaces, we establish explicit nonasymptotic free energy bounds controlled by first two moment discrepancies and local third moments. A perturbation-and-convexity argument transfers these comparisons to sandwich bounds for posterior mean squared error and posterior variance, including one-sided conclusions at nondifferentiable phase transitions. In high-dimensional product models, these conditions reduce to local moment controls and a canonical feature-radius scaling. Under weak regularity requirements, the resulting universality theory applies to a broad class of likelihood models, ranging from exponential families to more general regular local log-likelihoods. The framework is illustrated on sparse Bernoulli hypergraph inference.

We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables. In particular, let OPT:=max_{σ_1,cdots,σ_n}Eleft[sum_{j=1}^{m}max_{iin S_j} X_iright], where X_i are Gaussian, S_jsubset[n] and sum_iσ_i^2=1, then our theoretical results include: - We characterize the optimal variance allocation -- it concentrates on a small subset of variables as |S_j| increases, - A polynomial time approximation scheme (PTAS) for computing OPT when m=1, and - An O(log n) approximation algorithm for computing OPT for general m>1. Such expectation maximization problems occur in diverse applications, ranging from utility maximization in auctions markets to learning mixture models in quantitative genetics.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Prediction of future movement of stock prices has always been a challenging task for the researchers. While the advocates of the efficient market hypothesis (EMH) believe that it is impossible to design any predictive framework that can accurately predict the movement of stock prices, there are seminal work in the literature that have clearly demonstrated that the seemingly random movement patterns in the time series of a stock price can be predicted with a high level of accuracy. Design of such predictive models requires choice of appropriate variables, right transformation methods of the variables, and tuning of the parameters of the models. In this work, we present a very robust and accurate framework of stock price prediction that consists of an agglomeration of statistical, machine learning and deep learning models. We use the daily stock price data, collected at five minutes interval of time, of a very well known company that is listed in the National Stock Exchange (NSE) of India. The granular data is aggregated into three slots in a day, and the aggregated data is used for building and training the forecasting models. We contend that the agglomerative approach of model building that uses a combination of statistical, machine learning, and deep learning approaches, can very effectively learn from the volatile and random movement patterns in a stock price data. We build eight classification and eight regression models based on statistical and machine learning approaches. In addition to these models, a deep learning regression model using a long-and-short-term memory (LSTM) network is also built. Extensive results have been presented on the performance of these models, and the results are critically analyzed.

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

Institutional investors have been increasing the allocation of the illiquid alternative assets such as private equity funds in their portfolios, yet there exists a very limited literature on cash flow forecasting of illiquid alternative assets. The net cash flow of private equity funds typically follow a J-curve pattern, however the timing and the size of the contributions and distributions depend on the investment opportunities. In this paper, we develop a benchmark model and present two novel approaches (direct vs. indirect) to predict the cash flows of private equity funds. We introduce a sliding window approach to apply on our cash flow data because different vintage year funds contain different lengths of cash flow information. We then pass the data to an LSTM/ GRU model to predict the future cash flows either directly or indirectly (based on the benchmark model). We further integrate macroeconomic indicators into our data, which allows us to consider the impact of market environment on cash flows and to apply stress testing. Our results indicate that the direct model is easier to implement compared to the benchmark model and the indirect model, but still the predicted cash flows align better with the actual cash flows. We also show that macroeconomic variables improve the performance of the direct model whereas the impact is not obvious on the indirect model.

Causal inference is often focused on average effects, which can hide important aspects of the effect distributions. Here we consider the entire posterior effects distribution by estimating full counterfactual outcome distributions. We propose a methodology for inference on counterfactual distributions which builds upon the martingale posterior framework of Fong et al. (2023). This provides a highly flexible approach to estimating densities, distribution functions, and derived quantities such as quantiles, which coherently quantifies the epistemic uncertainty on any target estimand of interest. As the predictive recursions are based on an underlying nonparametric model (a Dirichlet process mixture model), our method naturally inherits robustness with respect to restrictive parametric assumptions. In addition, implementation of our method is typically very fast. This approach can be applied to marginal or conditional counterfactual distributions and is easily extended to an instrumental variables setup. Using the concept of almost conditionally identically distributed random variables, we prove convergence of the martingale posterior inference on the counterfactual outcome distributions for the causal models considered in the paper. We illustrate our approach on both simulated and real data. Using the latter, we investigate the effect of zinc lozenges on common cold duration, the impact of vitamin A supplementation on children's survival rates with one-sided non-compliance (analysed in Imbens and Rubin, 1997a) and the effect of job training (LaLonde, 1986).

This survey delves into the application of diffusion models in time-series forecasting. Diffusion models are demonstrating state-of-the-art results in various fields of generative AI. The paper includes comprehensive background information on diffusion models, detailing their conditioning methods and reviewing their use in time-series forecasting. The analysis covers 11 specific time-series implementations, the intuition and theory behind them, the effectiveness on different datasets, and a comparison among each other. Key contributions of this work are the thorough exploration of diffusion models' applications in time-series forecasting and a chronologically ordered overview of these models. Additionally, the paper offers an insightful discussion on the current state-of-the-art in this domain and outlines potential future research directions. This serves as a valuable resource for researchers in AI and time-series analysis, offering a clear view of the latest advancements and future potential of diffusion models.

One of the challenging research problems in the domain of time series analysis and forecasting is making efficient and robust prediction of stock market prices. With rapid development and evolution of sophisticated algorithms and with the availability of extremely fast computing platforms, it has now become possible to effectively extract, store, process and analyze high volume stock market time series data. Complex algorithms for forecasting are now available for speedy execution over parallel architecture leading to fairly accurate results. In this paper, we have used time series data of the two sectors of the Indian economy: Consumer Durables sector and the Small Cap sector for the period January 2010 to December 2015 and proposed a decomposition approach for better understanding of the behavior of each of the time series. Our contention is that various sectors reveal different time series patterns and understanding them is essential for portfolio formation. Further, based on this structural analysis, we have also proposed several robust forecasting techniques and analyzed their accuracy in prediction using suitably chosen training and test data sets. Extensive results are presented to demonstrate the effectiveness of our propositions.

We present DEF (\ul{D}iffusion-augmented \ul{E}nsemble \ul{F}orecasting), a novel approach for generating initial condition perturbations. Modern approaches to initial condition perturbations are primarily designed for numerical weather prediction (NWP) solvers, limiting their applicability in the rapidly growing field of machine learning for weather prediction. Consequently, stochastic models in this domain are often developed on a case-by-case basis. We demonstrate that a simple conditional diffusion model can (1) generate meaningful structured perturbations, (2) be applied iteratively, and (3) utilize a guidance term to intuitivey control the level of perturbation. This method enables the transformation of any deterministic neural forecasting system into a stochastic one. With our stochastic extended systems, we show that the model accumulates less error over long-term forecasts while producing meaningful forecast distributions. We validate our approach on the 5.625^circ ERA5 reanalysis dataset, which comprises atmospheric and surface variables over a discretized global grid, spanning from the 1960s to the present. On this dataset, our method demonstrates improved predictive performance along with reasonable spread estimates.

State-space models (SSMs) provide a flexible framework for modelling time-series data. Consequently, SSMs are ubiquitously applied in areas such as engineering, econometrics and epidemiology. In this paper we provide a fast approach for approximate Bayesian inference in SSMs using the tools of deep learning and variational inference.

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM.

Completely randomized experiments, originally developed by Fisher and Neyman in the 1930s, are still widely used in practice, even in online experimentation. However, such designs are of limited value for answering standard questions in marketplaces, where multiple populations of agents interact strategically, leading to complex patterns of spillover effects. In this paper, we derive the finite-sample properties of tractable estimators for "Simple Multiple Randomization Designs" (SMRDs), a new class of experimental designs which account for complex spillover effects in randomized experiments. Our derivations are obtained under a natural and general form of cross-unit interference, which we call "local interference". We discuss the estimation of main effects, direct effects, and spillovers, and present associated central limit theorems.

Many production processes are characterized by numerous and complex cause-and-effect relationships. Since they are only partially known they pose a challenge to effective process control. In this work we present how Structural Equation Models can be used for deriving cause-and-effect relationships from the combination of prior knowledge and process data in the manufacturing domain. Compared to existing applications, we do not assume linear relationships leading to more informative results.

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for accounting for spatio-temporal variation that is not explained by observable predictor variables. We also show how estimation and prediction can be done in a computationally efficient manner. In an application to a large U.S. mortgage credit risk data set, we find that both predictive default probabilities for individual loans and predictive loan portfolio loss distributions obtained with our novel approach are more accurate compared to conventional independent linear hazard models and also linear spatio-temporal models. Using interpretability tools for machine learning models, we find that the likely reasons for this outperformance are strong interaction and non-linear effects in the predictor variables and the presence of large spatio-temporal frailty effects.

A core goal of computational social science is to discover interpretable differences in how language varies across outcomes of interest, such as political affiliation or instructional quality. Recent LLM-based hypothesis generation methods describe such differences in natural language, but select for globally discriminative patterns without accounting for covariates that shape the data based on researchers' domain knowledge. When covariates are ignored, selected patterns can reflect confounds rather than differences of substantive interest. We introduce conditional hypothesis generation, a framework that incorporates researcher-specified covariates to steer hypothesis discovery toward differences that hold within relevant subgroups. Two challenges arise: the target subgroup may be underrepresented (stratum imbalance), and the direction of a difference may reverse across subgroups (sign reversal). We propose two econometrics-inspired methods: one introduces feature--covariate interactions to detect sign reversals, and the other applies within-stratum demeaning and inverse-frequency reweighting to equalize underrepresented strata. Synthetic experiments show each method outperforms global baselines in its targeted setting, and expert evaluation on two real-world datasets confirms that covariate-aware generation surfaces more useful hypotheses within relevant subgroups.

Process analytics is an umbrella of data-driven techniques which includes making predictions for individual process instances or overall process models. At the instance level, various novel techniques have been recently devised, tackling next activity, remaining time, and outcome prediction. At the model level, there is a notable void. It is the ambition of this paper to fill this gap. To this end, we develop a technique to forecast the entire process model from historical event data. A forecasted model is a will-be process model representing a probable future state of the overall process. Such a forecast helps to investigate the consequences of drift and emerging bottlenecks. Our technique builds on a representation of event data as multiple time series, each capturing the evolution of a behavioural aspect of the process model, such that corresponding forecasting techniques can be applied. Our implementation demonstrates the accuracy of our technique on real-world event log data.

Recognizing that traditional forecasting models often rely solely on historical demand, this work investigates the potential of data-driven techniques to automatically select and integrate market indicators for improving customer demand predictions. By adopting an exploratory methodology, we integrate macroeconomic time series, such as national GDP growth, from the Eurostat database into Neural Prophet and SARIMAX forecasting models. Suitable time series are automatically identified through different state-of-the-art feature selection methods and applied to sales data from our industrial partner. It could be shown that forecasts can be significantly enhanced by incorporating external information. Notably, the potential of feature selection methods stands out, especially due to their capability for automation without expert knowledge and manual selection effort. In particular, the Forward Feature Selection technique consistently yielded superior forecasting accuracy for both SARIMAX and Neural Prophet across different company sales datasets. In the comparative analysis of the errors of the selected forecasting models, namely Neural Prophet and SARIMAX, it is observed that neither model demonstrates a significant superiority over the other.

This paper considers the problem of variable selection allowing for parameter instability. It distinguishes between signal and pseudo-signal variables that are correlated with the target variable, and noise variables that are not, and investigate the asymptotic properties of the One Covariate at a Time Multiple Testing (OCMT) method proposed by Chudik et al. (2018) under parameter insatiability. It is established that OCMT continues to asymptotically select an approximating model that includes all the signals and none of the noise variables. Properties of post selection regressions are also investigated, and in-sample fit of the selected regression is shown to have the oracle property. The theoretical results support the use of unweighted observations at the selection stage of OCMT, whilst applying down-weighting of observations only at the forecasting stage. Monte Carlo and empirical applications show that OCMT without down-weighting at the selection stage yields smaller mean squared forecast errors compared to Lasso, Adaptive Lasso, and boosting.

We propose a statistical framework built on latent variable modeling for scaling laws of large language models (LLMs). Our work is motivated by the rapid emergence of numerous new LLM families with distinct architectures and training strategies, evaluated on an increasing number of benchmarks. This heterogeneity makes a single global scaling curve inadequate for capturing how performance varies across families and benchmarks. To address this, we propose a latent variable modeling framework in which each LLM family is associated with a latent variable that captures the common underlying features in that family. An LLM's performance on different benchmarks is then driven by its latent skills, which are jointly determined by the latent variable and the model's own observable features. We develop an estimation procedure for this latent variable model and establish its statistical properties. We also design efficient numerical algorithms that support estimation and various downstream tasks. Empirically, we evaluate the approach on 12 widely used benchmarks from the Open LLM Leaderboard (v1/v2).

We present a new approach to formulating and solving heterogeneous agent models with aggregate risk. We replace the cross-sectional distribution with low-dimensional prices as state variables and let agents learn equilibrium price dynamics directly from simulated paths. To do so, we introduce a structural reinforcement learning (SRL) method which treats prices via simulation while exploiting agents' structural knowledge of their own individual dynamics. Our SRL method yields a general and highly efficient global solution method for heterogeneous agent models that sidesteps the Master equation and handles problems traditional methods struggle with, in particular nontrivial market-clearing conditions. We illustrate the approach in the Krusell-Smith model, the Huggett model with aggregate shocks, and a HANK model with a forward-looking Phillips curve, all of which we solve globally within minutes.

Pre-trained Large Language Models (LLMs) encapsulate large amounts of knowledge and take enormous amounts of compute to train. We make use of this resource, together with the observation that LLMs are able to transfer knowledge and performance from one domain or even modality to another seemingly-unrelated area, to help with multivariate demand time series forecasting. Attention in transformer-based methods requires something worth attending to -- more than just samples of a time-series. We explore different methods to map multivariate input time series into the LLM token embedding space. In particular, our novel multivariate patching strategy to embed time series features into decoder-only pre-trained Transformers produces results competitive with state-of-the-art time series forecasting models. We also use recently-developed weight-based diagnostics to validate our findings.

Understanding memorisation in language models has practical and societal implications, e.g., studying models' training dynamics or preventing copyright infringements. Prior work defines memorisation as the causal effect of training with an instance on the model's ability to predict that instance. This definition relies on a counterfactual: the ability to observe what would have happened had the model not seen that instance. Existing methods struggle to provide computationally efficient and accurate estimates of this counterfactual. Further, they often estimate memorisation for a model architecture rather than for a specific model instance. This paper fills an important gap in the literature, proposing a new, principled, and efficient method to estimate memorisation based on the difference-in-differences design from econometrics. Using this method, we characterise a model's memorisation profile--its memorisation trends across training--by only observing its behaviour on a small set of instances throughout training. In experiments with the Pythia model suite, we find that memorisation (i) is stronger and more persistent in larger models, (ii) is determined by data order and learning rate, and (iii) has stable trends across model sizes, thus making memorisation in larger models predictable from smaller ones.

We develop a data-driven information-theoretic framework for sharp partial identification of causal effects under unmeasured confounding. Existing approaches often rely on restrictive assumptions, such as bounded or discrete outcomes; require external inputs (for example, instrumental variables, proxies, or user-specified sensitivity parameters); necessitate full structural causal model specifications; or focus solely on population-level averages while neglecting covariate-conditional effects. We overcome all four limitations simultaneously by establishing novel information-theoretic, data-driven divergence bounds. Our key theoretical contribution shows that the f-divergence between the observational distribution P(Y | A = a, X = x) and the interventional distribution P(Y | do(A = a), X = x) is upper bounded by a function of the propensity score alone. This result enables sharp partial identification of conditional causal effects directly from observational data, without requiring external sensitivity parameters, auxiliary variables, full structural specifications, or outcome boundedness assumptions. For practical implementation, we develop a semiparametric estimator satisfying Neyman orthogonality (Chernozhukov et al., 2018), which ensures root-n consistent inference even when nuisance functions are estimated via flexible machine learning methods. Simulation studies and real-world data applications, implemented in the GitHub repository (https://github.com/yonghanjung/Information-Theretic-Bounds), demonstrate that our framework provides tight and valid causal bounds across a wide range of data-generating processes.

Volatility clustering is a crucial property that has a substantial impact on stock market patterns. Nonetheless, developing robust models for accurately predicting future stock price volatility is a difficult research topic. For predicting the volatility of three equities listed on India's national stock market (NSE), we propose multiple volatility models depending on the generalized autoregressive conditional heteroscedasticity (GARCH), Glosten-Jagannathan-GARCH (GJR-GARCH), Exponential general autoregressive conditional heteroskedastic (EGARCH), and LSTM framework. Sector-wise stocks have been chosen in our study. The sectors which have been considered are banking, information technology (IT), and pharma. yahoo finance has been used to obtain stock price data from Jan 2017 to Dec 2021. Among the pulled-out records, the data from Jan 2017 to Dec 2020 have been taken for training, and data from 2021 have been chosen for testing our models. The performance of predicting the volatility of stocks of three sectors has been evaluated by implementing three different types of GARCH models as well as by the LSTM model are compared. It has been observed the LSTM performed better in predicting volatility in pharma over banking and IT sectors. In tandem, it was also observed that E-GARCH performed better in the case of the banking sector and for IT and pharma, GJR-GARCH performed better.