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On Backshift-Operator Polynomial Transformations to Stationarity for Single- and Multi-Component Time Series
On Backshift-Operator Polynomial Transformations to Stationarity for Single- and Multi-Component Time Series
RR82-08
Abstract
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. Counter-examples are presented to show that continuity assumptions on the spectral distribution functions involved are necessary to obtain these results.
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Statistical Research Reports and Studies
Page Last Revised - February 11, 2025
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