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A multivariate extension of the Misspecification-Resistant Information Criterion

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  • Gery Andr'es D'iaz Rubio
  • Simone Giannerini
  • Greta Goracci

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.

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  • Gery Andr'es D'iaz Rubio & Simone Giannerini & Greta Goracci, 2022. "A multivariate extension of the Misspecification-Resistant Information Criterion," Papers 2202.09225, arXiv.org.
    • Handle: RePEc:arx:papers:2202.09225
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    References listed on IDEAS

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    1. Bessler, Wolfgang & Leonhardt, Alexander & Wolff, Dominik, 2016. "Analyzing hedging strategies for fixed income portfolios: A Bayesian approach for model selection," International Review of Financial Analysis, Elsevier, vol. 46(C), pages 239-256.
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