Recursive Parameter Estimation for ARMA Simulations

Abstract

The parameter estimation algorithms for the autoregressive moving average (ARMA) simulation of multivariate random processes is considered. The recursive procedure for estimating the parameters of multivariate AR models is extended to the parameter estimation of multivariate ARMA models of same order for both the AR and MA components, which are usually used in the ARMA simulation of stationary multivariate random processes. The recursive parameter estimation procedure for ARMA models relies on the knowledge of the input-output cross correlation of the model, which is obtained with a procedure from the two-stage least-squares method, in that an AR model of high order is used to estimate the cross correlation. A numerical example shows that the recursive procedure for multivariate ARMA models leads to good ARMA representation of random processes, which is characterized by a specified target spectrum.