General Hannan and Quinn Criterion for Common Time Series
This work provides improved model selection tools for researchers and practitioners working with complex time series data, ensuring more accurate model identification.
This paper introduces new data-driven model selection criteria for a broad range of time series models, including ARMA, GARCH, and APARCH processes. The criteria are designed to be adaptive and achieve strong consistency, meaning they select the true model almost surely asymptotically.
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.