Optimal order for signal and system modeling

Abstract

Given a data set, the problem of designing a dynamic model either for an observed signal or for an input/output system appears in numerous situations where no physical model is available. The performance of this fitting crucially depends on the model class used. In this paper, the very first issue-that of model order selection-is addressed. Interestingly, the best performance realizable can be estimated directly from the data, without having to choose and test different model classes. An estimator of this performance bound for each order is proposed, allowing the determination of the optimal order, irrespectively of any specific model class.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>