Universal linear prediction by model order weighting

A common problem that arises in adaptive filtering, autoregressive modeling , or linear prediction is the selection of an appropriate order for the und erlying linear parametric model. We address this problem for linear predict ion, but instead of fixing a specific model order, we develop a sequential prediction algorithm whose sequentially accumulated average squared predict ion error for any bounded individual sequence is as good as the performance attainable by the best sequential linear predictor of order less than some M, This predictor is found by transforming linear prediction into a proble m analogous to the sequential probability assignment problem from universal coding theory. The resulting universal predictor uses essentially a perfor mance-weighted average of all predictors for model orders less than:M.:Effi cient lattice filters are used to generate the predictions:of all the model s recursively, resulting in a complexity of the universal algorithm that is no larger than that of the largest model order. Examples of prediction per formance are provided for autoregressive and speech data as well as an exam ple of adaptive data equalization.