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November, 1975 Noninvertible Transfer Functions and their Forecasts
David A. Pierce
Ann. Statist. 3(6): 1354-1360 (November, 1975). DOI: 10.1214/aos/1176343290


A transfer function relating a time series $y_t$ to present and past values of a series $x_t$ need not possess an inverse. When $(x_t, y_t)$ is a covariance stationary process, it is shown that noninvertibility in this transfer function has the effect of reducing the error variance of the minimum mean-square-error predictor of $y_t$ one or more steps ahead. In deriving these results a "dual" series to $x_t$ is constructed, which has univariate stochastic structure identical to that of $x_t$ itself, and an associated dual transfer function relating it to $y_t$ which is invertible.


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David A. Pierce. "Noninvertible Transfer Functions and their Forecasts." Ann. Statist. 3 (6) 1354 - 1360, November, 1975.


Published: November, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0323.62063
MathSciNet: MR519102
Digital Object Identifier: 10.1214/aos/1176343290

Primary: 62M20
Secondary: 62M10

Keywords: distributed lag models , dynamic models , forecasting , invertibility (of transfer function models) , prediction , Transfer-function models

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 6 • November, 1975
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