  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.
