Efficient and Consistent Data-Driven Model Selection for Time Series

TL;DR

This paper develops a data-driven model selection method for causal time series, demonstrating its superior consistency and efficiency over traditional criteria like AIC and BIC through theoretical analysis and simulations.

Contribution

It introduces a new penalty-based model selection criterion, KC', derived from Bayesian principles, with proven asymptotic properties and improved performance in time series analysis.

Findings

KC' outperforms AIC and BIC in consistency and efficiency.

Theoretical results confirm the asymptotic optimality of the proposed criterion.

Monte-Carlo experiments validate the practical advantages of KC'.

Abstract

This paper studies the model selection problem in a large class of causal time series models, which includes both the ARMA or AR($\infty$) processes, as well as the GARCH or ARCH($\infty$), APARCH, ARMA-GARCH and many others processes. We first study the asymptotic behavior of the ideal penalty that minimizes the risk induced by a quasi-likelihood estimation among a finite family of models containing the true model. Then, we provide general conditions on the penalty term for obtaining the consistency and efficiency properties. We notably prove that consistent model selection criteria outperform classical AIC criterion in terms of efficiency. Finally, we derive from a Bayesian approach the usual BIC criterion, and by keeping all the second order terms of the Laplace approximation, a data-driven criterion denoted KC'. Monte-Carlo experiments exhibit the obtained asymptotic results and show that KC' criterion does better than the AIC and BIC ones in terms of consistency and efficiency.