  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.
