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Abstract:
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Multivariate signal extraction can be accomplished through the use of latent component models, for which typically the number of parameters increases quadratically with dimension. Heuristically, this is because the linear filtering theory is built upon knowledge of variance and covariances. One approach is to use the EM algorithm to implicitly compute maximum likelihood estimates (MLEs), or perhaps approximate the true MLEs. EM, or Expectation-Maximization, proceeds by the concept of a full data likelihood which in this context amounts to considering the data jointly with the signals of interest. In this research we investigate the case of component models driven by vector white noise. We show the M-step yields an explicit formula for the white noise covariance matrices. This allows parameters to be computed from knowledge of the extracted signal and the error covariances. This formula is fast to compute (no matrix inversions), and hence the speed of the method depends on our facility with signal extraction. This model and algorithm are applied to a vector-valued daily immigration series.
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