A NOTE ON THE GENERATION OF INDEPENDENT REALIZATIONS OF A VECTOR AUTOREGRESSIVE MOVING‐AVERAGE PROCESS
B. L. Shea · Journal of Time Series Analysis · 1988
Abstract. Barone has described a method for generating independent realizations of a vector autoregressive moving‐average (ARMA) process which involves recasting the ARMA model in state space form. We discuss a direct method of computing the initial state covariance matrix T0 which, unless the number of time series is large, is usually faster than using the doubling algorithm of Anderson and Moore. Our numerical comparisons are particularly valuable because T0 must also be computed when calculating the likelihood function. A number of other computational refinements are described. In particular, we advocate the use of Choleski factorizations rather than spectral decompositions. For a pure moving‐average process computational savings can be achieved by working directly with the ARMA model rather than with its state space representation.