Systems and Control
Amenities & Services
City & Area
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.
Comments on this page are welcome and may be emailed to
Updating responsibility Arun Chotai. This page is copyright of Lancaster University.
12/10/01 - PGM.