General Hannan and Quinn criterion for common time series

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