Lag length identification for VAR models with non-constant variance

TL;DR

This paper develops an adaptive AIC method for accurately identifying the lag length in VAR models with time-varying variance, improving over standard tools that are not justified under heteroscedasticity.

Contribution

It introduces a robust adaptive AIC and corrected confidence bounds for PAM and PCM tailored for models with unconditional heteroscedasticity.

Findings

Adaptive AIC outperforms standard AIC in simulations

Adaptive PAM and PCM are more accurate than OLS-based methods

Application to US finance data demonstrates practical utility

Abstract

The identification of the lag length for vector autoregressive models by mean of Akaike Information Criterion (AIC), Partial Autoregressive and Correlation Matrices (PAM and PCM hereafter) is studied in the framework of processes with time varying variance. It is highlighted that the use of the standard tools are not justified in such a case. As a consequence we propose an adaptive AIC which is robust to the presence of unconditional heteroscedasticity. Corrected confidence bounds are proposed for the usual PAM and PCM obtained from the Ordinary Least Squares (OLS) estimation. The volatility structure of the innovations is used to develop adaptive PAM and PCM. We underline that the adaptive PAM and PCM are more accurate than the OLS PAM and PCM for identifying the lag length of the autoregressive models. Monte Carlo experiments show that the adaptive $AIC$ have a greater ability to select the correct autoregressive order than the standard AIC. An illustrative application using US international finance data is presented.