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On Backshift-Operator Polynomial Transformations to Stationarity for Single- and Multi-Component Time Series

By Findley, David F.

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Statistical Reference Document

Excerpt
Excerpt: It is demonstrated that any two backshift operator polynomials which transform a given non-stationary time series into stationary series with continuous spectral distributions must have a common divisor which has this property. It follows that the lowest-degree polynomial with this property is unique to within a constant multiple. Using this result some derivations are given, under varying assumptions, of a transformation formula used in non-stationary signal extraction. Counterexamples are presented to show that continuity assumptions on the spectral distribution functions involved are necessary to obtain these results. 1. Introduction. It is a common practice in the analysis of a nonstationary time series to look for a polynomial in the backshift operator B, such as p(B) = (l-B)(l-B12), normalized by p(O)=l, which transforms the given series into a stationary series (Box and Jenkins, 1976). It appears to have been taken for granted that when such a polynomial can be found, then after superfluous factors (e ...

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Book Id: WPLBN0000598558
Format Type: PDF eBook
File Size: 718,268 KB.
Reproduction Date: 2005
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Title: On Backshift-Operator Polynomial Transformations to Stationarity for Single- and Multi-Component Time Series  
Author: Findley, David F.
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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