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.
翻译:本文旨在研究大量时间序列的数据驱动模式选择标准,其中包括ARMA或AR($/infty$)程序,以及GARCH或ARCH($/infty$)、APARCH和其他许多程序。我们处理了设计适应性标准这一具有很强一致性特性的棘手问题。当从上述一个模型中得出观测结果时,新的标准几乎肯定不同时选择真正的模型。拟议标准的基础是尽量减少与汉南和Quinn标准相似的受罚对比,然后涉及一个在大多数经典时间序列模型和较为复杂的模型中已知的术语,这个术语可以由数据驱动。Monte-Carlo实验和CAC 40指数的一个示例都用来突出所获得的结果。