Computation of Theoretical Autocovariance Matrices of Multivariate Autoregressive Moving Average Time Series
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1990 · Volume 52 · Issue 1
DOI: 10.1111/j.2517-6161.1990.tb01778.x
Abstract
Matrix expressions relating the theoretical autocovariances of autoregressive moving average (ARMA) processes to their parameters are derived and used to design an efficient procedure for computing autocovariance sequences of multivariate ARMA processes. The method proposed is more efficient than others suggested in the literature and, in particular, reduces the computational burden associated with exact maximum likelihood estimation of ARMA models. The closed form expressions facilitate the implementation of algorithms for computing multivariate autocovariances.
Keywords
autoregressive moving average processes, exact maximum likelihood, multivariate time series, theoretical autocovariances
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