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Copulas and long memory

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Title: Copulas and long memory
Authors: Ibragimov, R
Lentzas, G
Item Type: Journal Article
Abstract: This paper focuses on the analysis of persistence propertiesof copula-based time series. We obtain theoretical results that demonstratethat Gaussian and Eyraud-Farlie-Gumbel-Morgenstern copulas always pro-duce short memory stationary Markov processes. We further show via sim-ulations that, in finite samples, stationary Markov processes, such as thosegenerated by Clayton copulas, may exhibit a spurious long memory-like be-havior on the level of copulas, as indicated by standard methods of inferenceand estimation for long memory time series. We also discuss applicationsof copula-based Markov processes to volatility modeling and the analysisof nonlinear dependence properties of returns in real financial markets thatprovide attractive generalizations of GARCH models. Among other conclu-sions, the results in the paper indicate non-robustness of the copula-levelanalogues of standard procedures for detecting long memory on the levelof copulas and emphasize the necessity of developing alternative inferencemethods.
Issue Date: 12-Dec-2017
Date of Acceptance: 1-Dec-2017
URI: http://hdl.handle.net/10044/1/67775
DOI: https://dx.doi.org/10.1214/14-PS233
ISSN: 1549-5787
Publisher: Institute of Mathematical Statistics
Start Page: 289
End Page: 327
Journal / Book Title: Probability Surveys
Volume: 14
Copyright Statement: Copyright for all articles in Probability Surveys is CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)
Keywords: 0102 Applied Mathematics
0104 Statistics
Publication Status: Published
Open Access location: https://doi.org/10.1214/14-PS233
Appears in Collections:Imperial College Business School