This paper studies the model selection problem in a large class of causal time series models, which includes both the ARMA or AR($\infty$) processes, as well as the GARCH or ARCH($\infty$), APARCH, ARMA-GARCH and many others processes. We first study the asymptotic behavior of the ideal penalty that minimizes the risk induced by a quasi-likelihood estimation among a finite family of models containing the true model. Then, we provide general conditions on the penalty term for obtaining the consistency and efficiency properties. We notably prove that consistent model selection criteria outperform classical AIC criterion in terms of efficiency. Finally, we derive from a Bayesian approach the usual BIC criterion, and by keeping all the second order terms of the Laplace approximation, a data-driven criterion denoted KC'. Monte-Carlo experiments exhibit the obtained asymptotic results and show that KC' criterion does better than the AIC and BIC ones in terms of consistency and efficiency.
翻译:本文研究大量因果时间序列模型的模型选择问题,这些模型包括ARMA或AR($/infty$)程序,以及GARCH或ARCH($/infty$)、APARCH、ARMA-GARCH和许多其他程序。我们首先研究在包含真实模型的有限模型组中将准类似估计引起的风险降到最低的理想惩罚的无症状行为。然后,我们为获得一致性和效率特性的惩罚条件提供一般条件。我们特别证明,一致的模型选择标准在效率方面优于典型的ACIC标准。最后,我们从巴伊西亚方法中得出通常的BIC标准,并保持Laplace近似值的所有第二顺序条件,即数据驱动标准,标明KC。Monte-Carlo实验显示了获得的无症状结果,并表明KC标准在一致性和效率方面优于AC和BIC标准。