Covariance matrix estimation for estimators of mixing weak ARMA models

For the statistical analysis of the ARMA models, the standard methods require that the linear innovations are martingale differences. This property is not satisfied for ARMA representations of non-linear processes. In such a case, the standard method typically entails an underestimation of the variance of the least-squares estimator of the ARMA parameters (and consequently it entails a serious risk of overparameterization). In this paper, the martingale difference assumption is relaxed. We propose a consistent estimator of the covariance matrix of the least-squares estimator under a mixing assumption on the observed process.