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The auto-regression and the moving-average
Authors:Chrysoula Dimitriou-Fakalou
Institution:Department of Statistical Science, University College London, Gower Street, London, UK
Abstract:We explore some relationships in the second-order properties of a causal auto-regression and an invertible moving-average process with the same polynomial. We reveal that the inverse variance matrix for random variables from the auto-regression is equal to a conditional variance matrix of Gaussian random variables from the moving-average and vice versa. While the inverse variance matrix for the auto-regression can be written explicitly, we manage to write down the exact Gaussian likelihood of consecutive observations from the moving-average process, by using the properties of the auto-regression.
Keywords:Gaussian likelihood  Innovations algorithm  Inverse variance matrix
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