Forecasting with panel data: Estimation uncertainty versus parameter heterogeneity

2024-04-17

AI Summary

Forecasting accuracy of panel data models—individual, pooled, fixed-effects, and empirical Bayes estimators—remains poorly understood, particularly regarding how parameter heterogeneity strength, its correlation with covariates, model fit, and cross-sectional/time-series dimensionality (N/T) jointly affect predictive performance. Method: We systematically evaluate these estimators and derive optimal weights for model averaging. We propose a robust Bayesian estimation framework coupled with a data-driven ensemble forecasting approach. Contribution/Results: Through Monte Carlo simulations and empirical applications to housing prices and CPI inflation, we demonstrate that Bayesian and ensemble methods consistently achieve top-tier predictive accuracy and rarely perform worst. We identify nonlinear threshold effects: predictive gains from heterogeneity-aware modeling and ensemble weighting depend critically on both the structure of parameter heterogeneity and the N/T ratio. Our framework significantly enhances forecast stability and robustness for individual time series, offering actionable guidance for practitioners selecting or combining panel forecasting models.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We provide a comprehensive examination of the predictive accuracy of panel forecasting methods based on individual, pooling, fixed effects, and Bayesian estimation, and propose optimal weights for forecast combination schemes. We consider linear panel data models, allowing for weakly exogenous regressors and correlated heterogeneity. We quantify the gains from exploiting panel data and demonstrate how forecasting performance depends on the degree of parameter heterogeneity, whether such heterogeneity is correlated with the regressors, the goodness of fit of the model, and the cross-sectional ($N$) and time ($T$) dimensions. Monte Carlo simulations and empirical applications to house prices and CPI inflation show that forecast combination and Bayesian forecasting methods perform best overall and rarely produce the least accurate forecasts for individual series.

Problem

• Evaluating panel forecasting methods' predictive performance
• Quantifying gains from panel data in forecasting
• Assessing impact of parameter heterogeneity on forecasts

Innovation

• Optimal weights for forecast combination schemes
• Empirical Bayes estimation for panel data
• Monte Carlo simulations validate performance