论文标题
一般因果时间序列的强稳定模型选择
Strong consistent model selection for general causal time series
论文作者
论文摘要
我们考虑了大型因果时间序列模型中模型选择的强烈一致问题，包括AR（$ \ infty $），Arch（$ \ infty $），TARCH（$ \ infty $），ARMA-GARCH和许多其他古典流程。 我们提出了基于模型的准可能性的惩罚标准。 我们提供足够的条件，以确保拟议程序的强大一致性。同样，所选模型参数的估计器遵守迭代对数定律。 看来，与Bardet {\ it等} \ Cite {Bardet2020}获得的弱一致性的结果不同，不需要正则化参数与模型结构之间的依赖性。
We consider the strongly consistent question for model selection in a large class of causal time series models, including AR($\infty$), ARCH($\infty$), TARCH($\infty$), ARMA-GARCH and many classical others processes. We propose a penalized criterion based on the quasi likelihood of the model. We provide sufficient conditions that ensure the strong consistency of the proposed procedure. Also, the estimator of the parameter of the selected model obeys the law of iterated logarithm. It appears that, unlike the result of the weak consistency obtained by Bardet {\it et al.} \cite{Bardet2020}, a dependence between the regularization parameter and the model structure is not needed.
