On testing for independence between generalized error models of several time series

[2410.24003] On testing for independence between generalized error models of several time series Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Methodology arXiv:2410.24003 (stat) [Submitted on 31 Oct 2024 ( v1 ), last revised 14 May 2026 (this version, v6)] Title: On testing for independence between generalized error models of several time series Authors: Kilani Ghoudi , Bouchra R. Nasri , Bruno N. Remillard View a PDF of the paper titled On testing for independence between generalized error models of several time series, by Kilani Ghoudi and Bouchra R. Nasri and Bruno N. Remillard View PDF HTML (experimental) Abstract: We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility models and regime-switching models. We also propose statistics for testing independence between the generalized errors of these models, extending previous results of Duchesne, Ghoudi and Remillard (2012) obtained for stochastic volatility models. We define families of empirical processes constructed from lagged generalized errors, and we show that their joint asymptotic distributions are Gaussian and independent of the estimated parameters of the individual time series. Moebius transformations of the empirical processes are used to obtain tractable covariances. Several tests statistics are then proposed, based on Cramer-von Mises statistics and dependence measures, as well as graphical methods to visualize the dependence. In addition, numerical experiments are performed to assess the power of the proposed tests. Finally, to show the usefulness of our methodologies, examples of applications for financial data and crime data are given to cover both discrete and continuous cases. ll developed methodologies are implemented in the CRAN package IndGenErrors. Subjects: Methodology (stat.ME) Cite as: arXiv:2410.24003 [stat.ME] (or arXiv:2410.24003v6 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2410.24003 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Bruno Remillard [ view email ] [v1] Thu, 31 Oct 2024 15:02:35 UTC (621 KB) [v2] Tue, 22 Apr 2025 08:00:05 UTC (252 KB) [v3] Thu, 9 Oct 2025 09:14:42 UTC (239 KB) [v4] Tue, 27 Jan 2026 18:06:58 UTC (239 KB) [v5] Sat, 11 Apr 2026 21:54:15 UTC (240 KB) [v6] Thu, 14 May 2026 14:41:11 UTC (77 KB) Full-text links: Access Paper: View a PDF of the paper titled On testing for independence between generalized error models of several time series, by Kilani Ghoudi and Bouchra R. Nasri and Bruno N. Remillard View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2024-10 Change to browse by: stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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