Stochastic unobserved component models for adaptive signal extraction and forecasting

• Main Authors: Young, P.C., Tych, W., Pedregal, D.J.
• Format: Conference Proceeding
• Language: English
• Subjects: Adaptive signal processing; Analysis of variance; Predictive models; Signal analysis; Signal processing; Signal restoration; Stochastic processes; Stochastic resonance; Time series analysis; White noise
• ISSN: 1089-3555; 2379-2329
• DOI: 10.1109/NNSP.1998.710653

This paper is concerned with adaptive, off-line signal processing and forecasting for nonstationary signals described by the unobserved component model y/sub t/=T/sub t/+S/sub t/+f(u/sub t/)+N/sub t/+e/sub t/, for e/sub t//spl sim/N{O, /spl sigma//sup 2/}, where y/sub t/ is the observed time series, T/sub t/ is a trend or low-frequency component, S/sub t/ is a periodic component possibly exhibiting temporal changes in both amplitude and phase, f(u/sub t/) captures the influence of a vector of exogenous variables u/sub t/, if necessary including stochastic, nonlinear static or dynamic relationships, N/sub t/ is a stochastic perturbation component, and e/sub t/ is an irregular component, normally defined for analytical convenience as a normally distributed Gaussian sequence with zero mean value and variance /spl sigma//sup 2/ (i.e. discrete-time white noise). In order to allow for nonstationarity in the time series y/sub t/, the various components, including T/sub t/, are characterised by stochastic time-varying parameters each of which is defined as a nonstationary stochastic variable. The paper describes a new and flexible approach to off-line signal processing based on a dynamic harmonic regression (DHR) model of the unobserved components (UC) type and illustrates its performance via a typical problem of audio signal restoration.