Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein-Uhlenbeck processes

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Title: Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein-Uhlenbeck processes
Authors: Nguyen, M
Veraart, A
Item Type: Journal Article
Abstract: While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a L´evy-driven spatio-temporal Ornstein-Uhlenbeck process by randomly varying its rate parameter to model both short-range and longrange dependence. This particular set-up allows for non-separable spatio-temporal correlations which are desirable for real applications, as well as flexible spatial covariances which arise from the shapes of influence regions. Theoretical properties such as spatio-temporal stationarity and second-order moments are established. An isotropic g-class is also used to illustrate how the memory of the process is related to the probability distribution of the rate parameter. We develop a simulation algorithm for the compound Poisson case which can be used to approximate other L´evy bases. The generalised method of moments is used for inference and simulation experiments are conducted with a view towards asymptotic properties.
Issue Date: 10-May-2018
Date of Acceptance: 5-Apr-2018
ISSN: 1744-2508
Publisher: Taylor & Francis
Start Page: 1023
End Page: 1052
Journal / Book Title: Stochastics: An International Journal of Probability and Stochastic Processes
Volume: 90
Issue: 7
Copyright Statement: © 2018 Informa UK Limited, trading as Taylor & Francis Group
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: FP7-PEOPLE-2012-CIG-321707
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Statistics & Probability
Long range dependence
Ornstein-Uhlenbeck process
compound Poisson
generalized method of moments
01 Mathematical Sciences
15 Commerce, Management, Tourism And Services
Publication Status: Published
Appears in Collections:Mathematics
Faculty of Natural Sciences

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