Strongly consistent model selection for general causal time series

We consider the issue of strong consistency for model selection in a large class causal time series models, including AR(∞), ARCH(∞), TARCH(∞), ARMA–GARCH and many other classical processes. propose penalized criterion based on quasi likelihood model. provide sufficient conditions that ensure proposed procedure. Also, estimator parameter selected obeys law iterated logarithm. It appears that, unlike result weak obtained by Bardet et al. (2020), dependence between regularization structure is not needed.