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Correlation models with long-range dependence

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Chunsheng Ma
Chunsheng Ma*
Affiliation:
Wichita State University
*
∗ Postal address: Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260-0033, USA. Email address: [email protected]
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Abstract

This paper is concerned with the correlation structure of a stationary discrete time-series with long memory or long-range dependence. Given a sequence of bounded variation, we obtain necessary and sufficient conditions for a function generated from the sequence to be a proper correlation function. These conditions are applied to derive various slowly decaying correlation models. To obtain correlation models with short-range dependence from an absolutely summable sequence, a simple method is introduced.

Keywords

Correlationlong memoryshort memoryslow decayspectral density

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 60G10: Stationary processes 60G18: Self-similar processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 370 - 382
Copyright
Copyright © Applied Probability Trust 2002 

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