OPTIMALITY IN THE ESTIMATION OF A MA SYSTEM FROM A LONG AR MODEL FOR SIMULATION STUDIES

The determination of moving average (MA) models from a prior autoregre ssive (AR) approximation of a specified (target) spectral matrix is ad dressed; this is done in context with the need to simulate ground shak ing and other natural phenomena as multivariate random processes. Firs t, an existing technique based on a direct modeling of the target expr ession is revisited. In this regard, the influence of the order of the prior AR approximation, and the number of its harmonics used in the d etermination of the MA model, is described. Further, a simple selectio n technique of these parameters is presented that leads to an optimum MA approximation. Next, the relationship between a method based on the Cholesky factorization of the covariance matrix and the present techn ique is investigated to derive additional insight into its convergence properties. Finally, an alternative modeling technique based on an AR representation of the inverse of the target spectral matrix is presen ted.