We introduce a state-space representation for vector autoregressive moving-average models that enables maximum likelihood estimation using the EM algorithm. We obtain closed-form expressions for both the E- and M-steps; the former requires the Kalman filter and a fixed-interval smoother, and the latter requires least squares-type regression. We show via simulations that our algorithm converges reliably to the maximum, whereas gradient-based methods often fail because of the highly nonlinear nature of the likelihood function. Moreover, our algorithm converges in a smaller number of function evaluations than commonly used direct-search routines. Overall, our approach achieves its largest performance gains when applied to models of high dimension. We illustrate our technique by estimating a high-dimensional vector moving-average model for an efficiency test of California's wholesale electricity market.

, , ,
Journal of Time Series Analysis

Metaxoglou, K, & Smith, A. (Aaron). (2007). Maximum likelihood estimation of VARMA models using a state-space em algorithm. Journal of Time Series Analysis, 28(5), 666–685. doi:10.1111/j.1467-9892.2007.00529.x