Covariance Matrix Estimation for Estimators of Mixing World's Arma.

For the statistical analysis of the ARMA models, the standard method requires that the linear innovations are martingale differences. This assumption is not satisfied for ARMA representations of non-linear processes. In such a case the standard method tipically entails an underestimation of the variance of the least squares estimator of the ARMA parameters. 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.