%0 Generic
%A Brockwell, Peter J.
%A Dahlhaus, Rainer
%C Heidelberg
%D 1998
%F heidok:20873
%K Recursive autoregression; Durbin-Levinson algorithm; Burg algorithm; linear prediction; subset modelling; multistep prediction
%R 10.11588/heidok.00020873
%T Generalized Durbin-Levinson and Burg Algorithms
%U https://archiv.ub.uni-heidelberg.de/volltextserver/20873/
%X 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.