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Generalized Durbin-Levinson and Burg Algorithms

Brockwell, Peter J. ; Dahlhaus, Rainer

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Abstract

We develop recursive algorithms for subset modelling and prediction which generalize the well-known Durbin-Levinson and Burg algorithms and include the univariate version of the subset Whittle algorithm of Penm and Terrell (1982). The results are derived using a basic property of orthogonal projections which leads to very simple derivations of the standard versions of the algorithms. As an application of the results, we obtain new and easily applied algorithms for the recursive calculation of the best linear h-step predictors (for any fixed h > 0) of an arbitrary process with known mean and covariance function.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 07 Jun 2016 08:37
Date: January 1998
Number of Pages: 21
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Recursive autoregression; Durbin-Levinson algorithm; Burg algorithm; linear prediction; subset modelling; multistep prediction
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
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