Signal Extraction for Nonstationary Time Series

By Bell, William R.

Description
Statistical Reference Document

Excerpt
Summary: The signal extraction problem in time series i s t o estimate s t given observations on z t = s t + n t (signal plus noise). The solution when s t and n t are stationary i s well known, having been first obtained independently by Kolmogorov and Wiener in the 1940?s. Their solution can be w r i t - ten (assuming normality and zero means) as E(st 1 { z t l ) = y s ( ~ ) y Z ( ~ ) - ? z t, where yS(F) and yZ(F) are the autocovariance generating functions of s t and z t and F i s the forward-shift operator. I n this paper we allow either st or nt or both t o be nonstationary. - We consider homogeneous or explosive nonstationarity described by models of the form 6(B)zt = wt, where 6 ( B ), a polynomial in the backshift operator B = F- 1, has zeroes on o r inside the u n i t c i r c l e and wt i s stationary. Similarly, we have ds(B)st = u t and Gn(B)nt = vt. The nonstationary analogue of the solut i o n t o the stationary signal extraction problem i s Rt = ~~(B)~~(F)Y,(F)Y,(F)-~z~, where G;(B) ...

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Book Id: WPLBN0000596585
Format Type: PDF eBook
File Size: 2,689,624 KB.
Reproduction Date: 2005
Full Text

Title:

Signal Extraction for Nonstationary Time Series

Author:

Bell, William R.

Volume:

Language:

English

Subject:

Government publications, Census., Census report

Collection:

U.S. Census Bureau Collection

Subcollection:

Historic
Publication Date:

Publisher:

U.S. Census Bureau Department

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