Multidimensional and strong Gevers-Wouters algorithm for estimating moving average parameters and its application to the construction of the ARMA innovation model (Q2766034)

The author extends the Gevers-Wouters (G-W) algorithm for estimating moving average (MA) parameters to a multidimensional and strong G-W algorithm and proves a sufficient frequency-domain condition for obtaining a stable MA process, i.e., that the related spectrum matrix is non-singular everywhere in the unit circle. (For the problem and the original G-W algorithm cf. [\textit{M. Gevers} and \textit{W. Wouters}, J. A 19, 90-110 (1978; Zbl 0381.93041)].) Its application to the construction of the autoregressive moving average (ARMA) innovation model is then proposed, where a more convenient sufficient time-domain condition to guarantee its MA polynomial matrix to be stable is given. A simulation example shows that the proposed multidimensional and strong G-W algorithm has a very fast convergence property and high precision in practical applications.