General Hannan and Quinn Criterion for Common Time Series

TL;DR

This paper develops a new data-driven model selection criterion for a broad class of time series models, ensuring strong consistency and accurate model identification in large samples.

Contribution

It introduces an adaptive, penalized contrast criterion based on Hannan and Quinn's approach, applicable to diverse time series including ARMA, GARCH, and their variants.

Findings

The new criterion is strongly consistent, selecting the true model almost surely asymptotically.

Monte Carlo experiments validate the effectiveness of the proposed method.

Application to CAC 40 index demonstrates practical utility.

Abstract

This paper aims to study data driven model selection criteria for a large class of time series, which includes ARMA or AR($\infty$) processes, as well as GARCH or ARCH($\infty$), APARCH and many others processes. We tackled the challenging issue of designing adaptive criteria which enjoys the strong consistency property. When the observations are generated from one of the aforementioned models, the new criteria, select the true model almost surely asymptotically. The proposed criteria are based on the minimization of a penalized contrast akin to the Hannan and Quinn's criterion and then involved a term which is known for most classical time series models and for more complex models, this term can be data driven calibrated. Monte-Carlo experiments and an illustrative example on the CAC 40 index are performed to highlight the obtained results.