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The exact initial covariance matrix of the state vector of a general \(MA(q)\) process. (English) Zbl 1328.62515
Summary: The finite moving-average process is studied in state-space form, and its stochastic structure is exploited to derive a closed-form analytic expression for the covariance matrix of the initial state vector. The results provide interesting insight into the state-space structure of moving-average processes, and they minimize the computational requirements for exact maximum-likelihood estimation via the Kalman filter.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
AS 154
Full Text: DOI
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