A multivariate extension of the Misspecification-Resistant Information Criterion

TL;DR

This paper extends the Misspecification-Resistant Information Criterion (MRIC) to multivariate time series with univariate predictors, providing theoretical guarantees and demonstrating its superiority over traditional criteria in misspecified models.

Contribution

The paper introduces a multivariate extension of MRIC, deriving new asymptotic expressions and proving its consistency and efficiency in model selection under misspecification.

Findings

The vectorial MRIC accurately identifies the best predictive model in misspecified scenarios.

The method achieves asymptotic efficiency and consistency.

Traditional criteria like AIC and BIC fail in misspecified multivariate contexts.

Abstract

The Misspecification-Resistant Information Criterion (MRIC) proposed in [H.-L. Hsu, C.-K. Ing, H. Tong: On model selection from a finite family of possibly misspecified time series models. The Annals of Statistics. 47 (2), 1061--1087 (2019)] is a model selection criterion for univariate parametric time series that enjoys both the property of consistency and asymptotic efficiency. In this article we extend the MRIC to the case where the response is a multivariate time series and the predictor is univariate. The extension requires novel derivations based upon random matrix theory. We obtain an asymptotic expression for the mean squared prediction error matrix, the vectorial MRIC and prove the consistency of its method-of-moments estimator. Moreover, we prove its asymptotic efficiency. Finally, we show with an example that, in presence of misspecification, the vectorial MRIC identifies the best predictive model whereas traditional information criteria like AIC or BIC fail to achieve the task.