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Young, P.C. and Pedregal, D.J. (1999) Recursive and en bloc approaches to signal extraction. Journal of Applied Statistics, 26, 103-128.

In the literature on Unobservable Component Models, three main statistical instruments have been used for signal extraction: Fixed Interval Smoothing (FIS) which derives from Kalman's seminal work on optimal state-space filter theory in the time domain; Wiener-Kolmogorov-Whittle Optimal Signal Extraction (OSE) theory, which is normally set in the frequency domain and dominates the field of classical statistics; and Regularisation , which was developed mainly by numerical analysts but is referred to as Smoothing in the statistical literature (e.g. smoothing splines, kernel smoothers and local regression). Although some minor recognition of the inter-relationship between these methods can be discerned from the literature, no clear discussion of their equivalence has appeared. This paper exposes clearly the inter-relationships between the three methods; highlights important properties of the smoothing filters used in signal extraction; and stresses the advantages of the FIS algorithms as a practical solution to signal extraction and smoothing problems. It also emphasises the importance of the classical OSE theory as an analytical tool for a better understanding of the problem of signal extraction.

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Updating responsibility Arun Chotai. This page is copyright of Lancaster University.
12/10/01 - PGM.