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

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  • 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
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    References listed on IDEAS

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    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.
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