Asymptotic distribution of the estimated parameters of an $\operatorname{ARMA}(p,q)$ process with mixing innovations

Abstract

In this paper, we consider an $\operatorname{ARMA}(p,q)$ model with stationary, $\phi$-mixing error variables having uniformly bounded fourth-order moments. Both the autoregressive and moving average components of the model involve stable and explosive roots. Estimating the autoregressive parameters using the instrumental variable technique and the moving average parameters using a derived autoregressive process, we derive the asymptotic distribution of the estimators.