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June, 1984 Signal Extraction for Nonstationary Time Series
William Bell
Ann. Statist. 12(2): 646-664 (June, 1984). DOI: 10.1214/aos/1176346512


The nonstationary signal extraction problem is to estimate $s_t$ given observations on $z_t = s_t + n_t$ (signal plus noise) when either $s_t$ or $n_t$ or both is nonstationary. Homogeneous or explosive nonstationary time series described by models of the form $\delta(B)z_t = w_t$ where $\delta(B)$ has zeroes on or inside the unit circle and $w_t$ is stationary are considered. For certain cases, approximate solutions to the nonstationary signal extraction problem have been given by Hannan (1967), Sobel (1967), and Cleveland and Tiao (1976). The paper gives exact solutions in the forms of expressions for $E(s_t\mid\{z_t\})$ and $\operatorname{Var}(s_t\mid\{z_t\})$ (assuming normality) under two sets of alternative assumptions regarding the generation of $z_t, s_t$, and $n_t$. Extensions to signal extraction with a finite number of observations, to the nonGaussian case, and to the multivariate case are discussed.


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William Bell. "Signal Extraction for Nonstationary Time Series." Ann. Statist. 12 (2) 646 - 664, June, 1984.


Published: June, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0745.62087
MathSciNet: MR740918
Digital Object Identifier: 10.1214/aos/1176346512

Primary: 62M10
Secondary: 60G35

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 2 • June, 1984
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