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Representations of continuous-time ARMA processes

Part of: Stochastic processes Applications

Published online by Cambridge University Press:  14 July 2016

Peter J. Brockwell
Peter J. Brockwell*
Affiliation:
Department of Statistics, Colorado State University, Fort Collins, CO 80523-1877, USA. Email address: pjbrock@stat.colostate.edu
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Abstract

Using the kernel representation of a continuous-time Lévy-driven ARMA (autoregressive moving average) process, we extend the class of nonnegative Lévy-driven Ornstein–Uhlenbeck processes employed by Barndorff-Nielsen and Shephard (2001) to allow for nonmonotone autocovariance functions. We also consider a class of fractionally integrated Lévy-driven continuous-time ARMA processes obtained by a simple modification of the kernel of the continuous-time ARMA process. Asymptotic properties of the kernel and of the autocovariance function are derived.

Keywords

Continuous-time ARMA processLévy processstochastic volatilitylong memoryfractional integration

MSC classification

Primary: 60G10: Stationary processes
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
Part 7. Time series analysis
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 375 - 382
Copyright
Copyright © Applied Probability Trust 2004 

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