Fast Linear Estimation Methods for Vector Autoregressive Moving‐average Models

Abstract

Three linear methods for estimating parameter values of vector autoregressive 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.

Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models

“…Finally, initial estimates may be conditional maximum likelihood estimates or those obtained with other fast linear estimation methods (e.g. Shea 1987;Koreisha and Pukkila 1989), although care must be taken to ensure that they are admissible.…”

New approximation for ARMA parameters estimate

“…Durbin's approximation generates an algorithm in which the MA coefficients are calculated from the coefficients of a long-order autoregression. Hannan and Rissanen [7] and Koreisha and Pukkila [8] extend Durbin's method to univariate and multivariate ARMA models, respectively. Tunnicliffe-Wilson [15], Reinsel et al [12] and DeFrutos and Serrano [3] propose similar approximate ML estimation methods.…”

Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models

“…To improve efficiency, De Frutos and Serrano (2002) also suggest a GLS procedure. In a simulation study, they show that their method outperforms the double regression proposed by Koreisha and Pukkila (1989). Though consistent, their method is not asymptotically efficient (in the Gaussian case), and identifiability issues are not considered.…”