  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.
