Misspecification-Resistant Information Criterion for multivariate time series

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Abstract

The model selection step is crucial in statistical modelling and the literature devoted to the problem is vast. In the time series framework, one is typically interested in forecasting and control. There are two main approaches to this problem: statistical testing (e.g. likelihood ratio tests), or information criteria. If prediction is the goal, the latter is favoured in practical applications. Starting from the seminal work of Akaike, the literature in the last fifty years has proposed different information criteria and their asymptotic properties. The focus of the project is to extend to multivariate time series the misspecification-resistant information criterion¹ (MRIC), recently developed for scalar time series models when the number of observations goes to infinity while the number of ‘true’ parameters is fixed. This criterion is important for at least two main reasons: first, it solves some long-standing open problems that trace back to the first works of Akaike; second, it is applicable to both linear and nonlinear processes, possibly in a high-dimensional setting. We show some preliminary results where we obtain an asymptotic expression for the mean-squared prediction error matrix, and present two examples for a bivariate time series model with one and two regressors. This decomposition features the same structure as in the scalar case and allows to write the MRIC in both cases. We also prove the consistency of the method-of-moments estimator for the matrices regarding the first case, indicating that it may also hold for the second case. Further research will involve the study of the asymptotic consistency and efficiency of the MRIC, and the consequences of model misspecification in the vectorial case. As a secondary goal, we provide a critical review of the model selection literature based upon information criteria for parametric, nonparametric, and multivariate time series models.

¹ H.-L. Hsu, C.-K. Ing, H. Tong: On model selection from a finite family of possibly misspecified time series models. Ann. Statist. 47 (2), 1061-1087 (2019)

Gli Organizzatori                                                                                                              Il Direttore
Prof. Christian Hennig                                                                                         Prof. Angela Montanari                                   Prof. Silvia Cagnone

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