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Long-memory continuous-time correlation models

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 introduces a rather general class of stationary continuous-time processes with long memory by randomizing the time-scale of short-memory processes. In particular, by randomizing the time-scale of continuous-time autoregressive and moving-average processes, many power-law decay and slow decay correlation functions are obtained.

Keywords

Continuous-time autoregressive and moving-average processlong-range dependencepower-law decayshort-range dependenceslow decayOrnstein–Uhlenbeck process

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 60G10: Stationary processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1133 - 1146
Copyright
Copyright © Applied Probability Trust 2003 

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