IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v187y2022ics0047259x21001354.html
   My bibliography  Save this article

Change-point problems for multivariate time series using pseudo-observations

Author

Listed:
  • Nasri, Bouchra R.
  • Rémillard, Bruno N.
  • Bahraoui, Tarik

Abstract

In this article we show that under weak assumptions, the change-point tests designed for independent random vectors can also be used with pseudo-observations for testing change-point in the joint distribution of non-observable random vectors, the associated copula, or the margins, without modifying the limiting distributions. In particular, change-point tests can be applied to the residuals of stochastic volatility models or conditional distribution functions applied to the observations, which are prime examples of pseudo-observations. Since the limiting distribution of test statistics depends on the unknown joint distribution function or its associated unknown copula when the dimension is greater than one, we also show that iid multipliers and traditional bootstrap can be used with pseudo-observations to approximate P-values for the test statistics. Numerical experiments are performed in order to compare the different statistics and bootstrapping methods. Examples of applications to change-point problems are given. The R package changepointTests (Nasri and Rémillard, 2021) includes all the methodologies proposed in this article.

Suggested Citation

  • Nasri, Bouchra R. & Rémillard, Bruno N. & Bahraoui, Tarik, 2022. "Change-point problems for multivariate time series using pseudo-observations," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:jmvana:v:187:y:2022:i:c:s0047259x21001354
    DOI: 10.1016/j.jmva.2021.104857
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X21001354
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2021.104857?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zaichao Du, 2016. "Nonparametric bootstrap tests for independence of generalized errors," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 55-83, February.
    2. Olivier Scaillet, 2005. "A Kolmogorov-Smirnov Type Test for Positive Quadrant Dependence," FAME Research Paper Series rp128, International Center for Financial Asset Management and Engineering.
    3. Rohmer, Tom, 2016. "Some results on change-point detection in cross-sectional dependence of multivariate data with changes in marginal distributions," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 45-54.
    4. Adams, Zeno & Füss, Roland & Glück, Thorsten, 2017. "Are correlations constant? Empirical and theoretical results on popular correlation models in finance," Journal of Banking & Finance, Elsevier, vol. 84(C), pages 9-24.
    5. Nasri, Bouchra R. & Rémillard, Bruno N., 2019. "Copula-based dynamic models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 107-121.
    6. Berkes, István & Gombay, Edit & Horváth, Lajos & Kokoszka, Piotr, 2004. "SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1140-1167, December.
    7. Bucher, Axel & Kojadinovic, Ivan & Rohmer, Tom & Segers, Johan, 2014. "Detecting changes in cross-sectional dependence in multivariate time series," LIDAM Reprints ISBA 2014020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Kilani Ghoudi & Bruno Rémillard, 2018. "Serial independence tests for innovations of conditional mean and variance models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 3-26, March.
    9. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    10. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    11. Holmes, Mark & Kojadinovic, Ivan & Quessy, Jean-François, 2013. "Nonparametric tests for change-point detection à la Gombay and Horváth," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 16-32.
    12. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Genest, Christian & Ghoudi, Kilani & Rémillard, Bruno, 1996. "A note on tightness," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 331-339, May.
    14. Wied, Dominik & Krämer, Walter & Dehling, Herold, 2012. "Testing For A Change In Correlation At An Unknown Point In Time Using An Extended Functional Delta Method," Econometric Theory, Cambridge University Press, vol. 28(3), pages 570-589, June.
    15. Bücher, Axel & Kojadinovic, Ivan & Rohmer, Tom & Segers, Johan, 2014. "Detecting changes in cross-sectional dependence in multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 111-128.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-François Quessy, 2019. "Consistent nonparametric tests for detecting gradual changes in the marginals and the copula of multivariate time series," Statistical Papers, Springer, vol. 60(3), pages 717-746, June.
    2. Nasri, Bouchra R., 2022. "Tests of serial dependence for multivariate time series with arbitrary distributions," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    3. Rohmer, Tom, 2016. "Some results on change-point detection in cross-sectional dependence of multivariate data with changes in marginal distributions," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 45-54.
    4. Bücher, Axel & Kojadinovic, Ivan & Rohmer, Tom & Segers, Johan, 2014. "Detecting changes in cross-sectional dependence in multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 111-128.
    5. Bucher, Axel & Kojadinovic, Ivan, 2013. "A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing," LIDAM Discussion Papers ISBA 2013029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Salim Bouzebda, 2023. "On Weak Convergence of the Bootstrap Copula Empirical Process with Random Resample Size," Stats, MDPI, vol. 6(1), pages 1-16, February.
    7. Kojadinovic, Ivan & Rohmer, Tom & Segers, Johan, 2013. "Detecting changes in cross-sectional dependence in multivariate time series," LIDAM Discussion Papers ISBA 2013051, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.
    9. Pape, Katharina & Wied, Dominik & Galeano, Pedro, 2016. "Monitoring multivariate variance changes," Journal of Empirical Finance, Elsevier, vol. 39(PA), pages 54-68.
    10. Aslanidis, Nektarios & Martinez, Oscar, 2021. "Correlation regimes in international equity and bond returns," Economic Modelling, Elsevier, vol. 97(C), pages 397-410.
    11. Seo, Juwon, 2018. "Tests of stochastic monotonicity with improved power," Journal of Econometrics, Elsevier, vol. 207(1), pages 53-70.
    12. Rongrong Li & Lihua Xiong & Cong Jiang & Wenbin Li & Chengkai Liu, 2023. "Quantifying multivariate flood risk under nonstationary condition," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 116(1), pages 1161-1187, March.
    13. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    14. Kojadinovic, Ivan & Stemikovskaya, Kristina, 2019. "Subsampling (weighted smooth) empirical copula processes," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 704-723.
    15. Nasri, Bouchra R. & Rémillard, Bruno N. & Bouezmarni, Taoufik, 2019. "Semi-parametric copula-based models under non-stationarity," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 347-365.
    16. Bücher, Axel & Jäschke, Stefan & Wied, Dominik, 2015. "Nonparametric tests for constant tail dependence with an application to energy and finance," Journal of Econometrics, Elsevier, vol. 187(1), pages 154-168.
    17. Berens, Tobias & Weiß, Gregor N.F. & Wied, Dominik, 2015. "Testing for structural breaks in correlations: Does it improve Value-at-Risk forecasting?," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 135-152.
    18. Hoga, Yannick, 2017. "Monitoring multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 105-121.
    19. Beare, Brendan K. & Seo, Juwon, 2020. "Randomization Tests Of Copula Symmetry," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1025-1063, December.
    20. Kiriliouk, Anna & Segers, Johan & Tsukahara, Hideatsu, 2019. "On Some Resampling Procedures with the Empirical Beta Copula," LIDAM Discussion Papers ISBA 2019012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:187:y:2022:i:c:s0047259x21001354. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.