Inference and model selection in general causal time series with exogenous covariates

In this paper, we study a general class of causal processes with exogenous covariates, including many classical such as the ARMA-GARCH, APARCH, ARMAX, GARCH-X and APARCH-X processes. Under some Lipschitz-type conditions, existence τ-weakly dependent strictly stationary ergodic solution is established. We provide conditions for strong consistency derive asymptotic distribution quasi-maximum likelihood estimator (QMLE), both when true parameter an interior point parameters space it belongs to boundary. A significance Wald-type test developed. This quite extensive includes nullity parameter’s components, which in particular, allows us assess relevance covariates. Relying on QMLE model, also propose penalized criterion address problem model selection class. The weak procedure are Finally, Monte Carlo simulations conducted numerically illustrate main results.