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Exact maximum-likelihood estimation of autoregressive models via the Kalman filter. (English) Zbl 1328.62542
Summary: The pth order autoregression is studied in state-space form, and a closed-form analytic expression is obtained for the unconditional covariance matrix of the initial state vector. It is shown that this covariance matrix depends only on the first \(p\) autocovariances, which makes exact maximum-likelihood estimation via the Kalman filter a straightforward task.

MSC:
62M20 Inference from stochastic processes and prediction
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Software:
AS 154
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