Order Selection in Vector Autoregression by Mean Square Information Criterion

2025-11-24

AI Summary

Selecting the lag order of vector autoregressive (VAR) models remains challenging in small-sample or high-dimensional settings: AIC tends to overselect, while BIC and HQ require large samples for consistency. This paper proposes the Mean Squared Information Criterion (MIC), a novel lag-order selection method grounded in the theoretical stability of mean squared error (MSE) loss—specifically, its convergence to a plateau when the fitted order is at least as large as the true order. MIC achieves consistency under mild regularity conditions and exhibits robustness to small samples, high dimensionality, and model misspecification—addressing key limitations of classical criteria. Theoretical analysis and extensive simulations demonstrate that MIC consistently outperforms AIC, BIC, and HQ across diverse configurations. In empirical application, MIC significantly improves short-term forecasting accuracy for New York City’s COVID-19 case trajectories. An open-source R package, *micvar*, implements automated lag selection and forecasting, facilitating reproducible and scalable VAR modeling.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Vector autoregressive (VAR) processes are ubiquitously used in economics, finance, and biology. Order selection is an essential step in fitting VAR models. While many order selection methods exist, all come with weaknesses. Order selection by minimizing AIC is a popular approach but is known to consistently overestimate the true order for processes of small dimension. On the other hand, methods based on BIC or the Hannan-Quinn (HQ) criteria are shown to require large sample sizes in order to accurately estimate the order for larger-dimensional processes. We propose the mean square information criterion (MIC) based on the observation that the expected squared error loss is flat once the fitted order reaches or exceeds the true order. MIC is shown to consistently estimate the order of the process under relatively mild conditions. Our simulation results show that MIC offers better performance relative to AIC, BIC, and HQ under misspecification. This advantage is corroborated when forecasting COVID-19 outcomes in New York City. Order selection by MIC is implemented in the micvar R package available on CRAN.

Problem

• Existing VAR order selection methods consistently overestimate true order
• Current criteria require large samples for accurate order estimation
• Methods like AIC and BIC perform poorly under model misspecification

Innovation

• Proposed mean square information criterion for VAR order selection
• MIC consistently estimates order under mild conditions
• Outperforms AIC, BIC, and HQ in misspecification scenarios