Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes. Issue 7 (3rd October 2018)

• Record Type: Journal Article
• Authors: Nguyen, Michele; Veraart, Almut E. D.
• Is Part Of: Stochastics. Volume 90:Issue 7(2018)
• Page Start: 1023
• Page End: 1052
• Publication Date: 2018-10-03
• Subjects: Long range dependence -- Ornstein–Uhlenbeck process -- spatio-temporal -- compound Poisson -- generalized method of moments; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2018.1466886
• Languages: English
• ISSNs: 1744-2508

Abstract

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 Lévy-driven spatio-temporal Ornstein–Uhlenbeck process by randomly varying its rate parameter to model both short-range and long-range 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 Lévy bases. The generalized method of moments is used for inference and simulation experiments are conducted with a view towards asymptotic properties.