Order Selection in Vector Autoregression by Mean Square Information Criterion

TL;DR

This paper introduces the mean square information criterion (MIC) for selecting the order of vector autoregressive models, demonstrating its consistency and superior performance over traditional criteria like AIC, BIC, and HQ, especially under misspecification.

Contribution

The paper proposes the MIC as a new order selection method for VAR models, showing its consistency and improved performance through simulations and real data application.

Findings

MIC consistently estimates the true VAR order under mild conditions.

MIC outperforms AIC, BIC, and HQ in simulations with misspecified models.

MIC provides better forecasting accuracy for COVID-19 outcomes in NYC.

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.