FAST LINEAR ESTIMATION METHODS FOR VECTOR AUTOREGRESSIVE MOVING‐AVERAGE MODELS

Sergio Koreisha and Tarmo Pukkila

Journal of Time Series Analysis, 1989, vol. 10, issue 4, 325-339

Abstract: Abstract. Three linear methods for estimating parameter values of vector auto‐regressive moving‐average (VARMA) models which are in general at least an order of magnitude faster than maximum likelihood estimation are developed in this paper. Simulation results for different model structures with varying numbers of component series and observations suggest that the accuracy of these procedures is in most cases comparable with maximum likelihood estimation. Procedures for estimating parameter standard error are also discussed and used for identification of nonzero elements in the VARMA polynomial structures. These methods can also be used to establish the order of the VARMA structure. We note, however, that the primary purpose of these estimates is to generate initial estimates for the nonzero parameters in order to reduce subsequent computational time of more efficient estimation procedures such as exact maximum likelihood.

Date: 1989
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