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Shapes of stationary autocovariances

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Robert Lund ,
Ying Zhao  and
Peter C. Kiessler
Robert Lund*
Affiliation:
Clemson University
Ying Zhao
Affiliation:
University of Georgia
Peter C. Kiessler*
Affiliation:
Clemson University
*
∗Postal address: Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA.
∗Postal address: Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA.
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Abstract

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This note introduces shape orderings for stationary time series autocorrelation and partial autocorrelation functions and explores some of their convergence rate ramifications. The shapes explored include decreasing hazard rate and new better than used, orderings that are familiar from stochastic processes settings. Time series models where these shapes arise are presented. The shapes are used to obtain explicit geometric convergence rates for mean squared errors of one-step-ahead forecasts.

Keywords

ARMA processautocorrelationconvergence ratelog-convexitymean squared errorNWUpartial autocorrelation

MSC classification

Primary: 60G10: Stationary processes
Secondary: 60G20: Generalized stochastic processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006 , pp. 1186 - 1193
Copyright
© Applied Probability Trust 2006 

Footnotes

∗∗∗

Current address: 2-2-502 Qingfeng Huajing Yuan, Haidian Qu, Beijing, 100085, P. R. China.

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