An indirect proof for the asymptotic properties of VARMA model estimators

Strong consistency and asymptotic normality of a Gaussian quasi-maximum likelihood estimator for the parameters causal, invertible, identifiable vector autoregressive-moving average (VARMA) model are established in an indirect way. The proof is based on similar results much wider class VARMA models with time-dependent coefficients, hence context non-stationary heteroscedastic time series. For that reason, avoids spectral analysis arguments does not make use ergodicity. presented also applicable to ARMA models.