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

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Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes. / Nguyen, Michele; Veraart, Almut E.D.
In: Stochastics, Vol. 90, No. 7, 03.10.2018, p. 1023-1052.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Harvard

Nguyen, M & Veraart, AED 2018, 'Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes', Stochastics, vol. 90, no. 7, pp. 1023-1052. https://doi.org/10.1080/17442508.2018.1466886

APA

Nguyen, M., & Veraart, A. E. D. (2018). Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes. Stochastics, 90(7), 1023-1052. https://doi.org/10.1080/17442508.2018.1466886

CBE

Nguyen M, Veraart AED. 2018. Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes. Stochastics. 90(7):1023-1052. https://doi.org/10.1080/17442508.2018.1466886

MLA

Nguyen, Michele and Almut E.D. Veraart. "Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes". Stochastics. 2018, 90(7). 1023-1052. https://doi.org/10.1080/17442508.2018.1466886

Vancouver

Nguyen M, Veraart AED. Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes. Stochastics. 2018 Oct 3;90(7):1023-1052. doi: 10.1080/17442508.2018.1466886

Author

Nguyen, Michele ; Veraart, Almut E.D. / Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes. In: Stochastics. 2018 ; Vol. 90, No. 7. pp. 1023-1052.

Bibtex

@article{0d5fd60f3c3445e89f98b7ca01bd3ec0,
title = "Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes",
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{\'e}vy-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 L{\'e}vy bases. The generalized method of moments is used for inference and simulation experiments are conducted with a view towards asymptotic properties.",
keywords = "compound Poisson, generalized method of moments, Long range dependence, Ornstein–Uhlenbeck process, spatio-temporal",
author = "Michele Nguyen and Veraart, {Almut E.D.}",
year = "2018",
month = oct,
day = "3",
doi = "10.1080/17442508.2018.1466886",
language = "English",
volume = "90",
pages = "1023--1052",
journal = "Stochastics: An International Journal of Probability and Stochastic Processes ",
issn = "1744-2508",
publisher = "Taylor & Francis ",
number = "7",

}

RIS

TY - JOUR

T1 - Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes

AU - Nguyen, Michele

AU - Veraart, Almut E.D.

PY - 2018/10/3

Y1 - 2018/10/3

N2 - 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.

AB - 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.

KW - compound Poisson

KW - generalized method of moments

KW - Long range dependence

KW - Ornstein–Uhlenbeck process

KW - spatio-temporal

UR - http://www.scopus.com/inward/record.url?scp=85046791051&partnerID=8YFLogxK

U2 - 10.1080/17442508.2018.1466886

DO - 10.1080/17442508.2018.1466886

M3 - Journal article

AN - SCOPUS:85046791051

VL - 90

SP - 1023

EP - 1052

JO - Stochastics: An International Journal of Probability and Stochastic Processes

JF - Stochastics: An International Journal of Probability and Stochastic Processes

SN - 1744-2508

IS - 7

ER -