Some asymptotic results for time series model selection

TL;DR

This paper investigates the asymptotic properties of a penalized model selection procedure for diverse time series models, including count and causal processes, establishing conditions for consistency and highlighting cases of non-consistency.

Contribution

It introduces a general penalized contrast method for time series model selection and provides new asymptotic results, including conditions for both consistency and non-consistency.

Findings

Established asymptotic weak and strong consistency results.

Identified penalty classes that do not guarantee consistency.

Applied results to count and multivariate autoregressive time series.

Abstract

We consider the model selection problem for a large class of time series models, including, multivariate count processes, causal processes with exogenous covariates. A procedure based on a general penalized contrast is proposed. Some asymptotic results for weak and strong consistency are established. The non consistency issue is addressed, and a class of penalty term, that does not ensure consistency is provided. Examples of continuous valued and multivariate count autoregressive time series are considered.