We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible autoregressive moving-average (ARMA) time series models, which were initially established by Hannan [Journal of Applied Probability (1973) vol. 10, pp....

We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible ARMA time series models, which were initially established by Hannan (1973) via the asymptotic properties of a Whittle's estimator. This also paves the way to...