On the criterion function for ARMA estimation
It is shown that the asymptotic maximum-likelihood estimators for the parameters of stationary ARMA-models fulfill the conditions of stationarity and invertibility. For the criterion function of the conditional least-squares estimators, a matrix representation with lower- triangular Toeplitz matrices is given. Using circulant matrices a matrix representation is given of the frequency domain approximation of the likelihood function. It is shown that in this two cases the conditions of stationarity and invertibility are not always satisfied. Further some methods for reducing the bias of the estimators in the case of small samples are discussed.
asymptotic maximum- likelihood estimators
scientific article; zbMATH DE number 445185
scientific article