IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v195y2023ics0047259x22001427.html
   My bibliography  Save this article

A distance-based test of independence between two multivariate time series

Author

Listed:
  • Chu, Ba

Abstract

We contribute to recent research on distance correlation by extending its capability to test for independence between two time series. The proposed test is a Portmanteau-type test based on double-centered distance cross-covariances. We show that the test statistic constructed in this way is asymptotically normal and pivotal under the null hypothesis of independence, and it is consistent under fixed alternative hypotheses of dependence. We also propose a fast wild bootstrap procedure that can significantly improve the performance of the asymptotic test in finite samples. An extensive Monte Carlo simulation study designed to compare the proposed test with other existing procedures shows that both the proposed test and its bootstrap version can achieve a good size and power performance for several data generating processes (DGPs), and they can significantly outperform other tests under model misspecification. An empirical application to illustrate the applicability of the proposed method is also given.

Suggested Citation

  • Chu, Ba, 2023. "A distance-based test of independence between two multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:jmvana:v:195:y:2023:i:c:s0047259x22001427
    DOI: 10.1016/j.jmva.2022.105151
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X22001427
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2022.105151?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. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    2. Leucht, Anne & Neumann, Michael H., 2013. "Dependent wild bootstrap for degenerate U- and V-statistics," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 257-280.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Marc Hallin & Abdessamad Saidi, 2005. "Testing non-correlation and non-causality between two multivariate ARMA time series," ULB Institutional Repository 2013/2129, ULB -- Universite Libre de Bruxelles.
    5. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages 2-18, September.
    6. Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2015. "A generalization of an integral arising in the theory of distance correlation," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 116-119.
    7. Hong, Yongmiao, 1996. "Testing for independence between two covariance stationary time series," MPRA Paper 108731, University Library of Munich, Germany.
    8. Yongmiao Hong, 2001. "Testing for Independence between Two stationary Time Series via the Empirical Characteristic Function," Annals of Economics and Finance, Society for AEF, vol. 2(1), pages 123-164, May.
    9. Zhou Zhou, 2012. "Measuring nonlinear dependence in time‐series, a distance correlation approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 438-457, May.
    10. K Fokianos & M Pitsillou, 2018. "Testing independence for multivariate time series via the auto-distance correlation matrix," Biometrika, Biometrika Trust, vol. 105(2), pages 337-352.
    11. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
    12. Bakirov, Nail K. & Rizzo, Maria L. & Szekely, Gábor J., 2006. "A multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1742-1756, September.
    13. Cheung, Yin-Wong & Ng, Lilian K., 1996. "A causality-in-variance test and its application to financial market prices," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 33-48.
    14. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
    15. Marc Hallin & Abdessamad Saidi, 2005. "Testing Non‐Correlation and Non‐Causality between Multivariate ARMA Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 83-105, January.
    16. Shun Yao & Xianyang Zhang & Xiaofeng Shao, 2018. "Testing mutual independence in high dimension via distance covariance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 455-480, June.
    17. Michael W. Robbins & Thomas J. Fisher, 2015. "Cross-Correlation Matrices for Tests of Independence and Causality Between Two Multivariate Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 459-473, October.
    18. Chafik Bouhaddioui & Roch Roy, 2006. "A Generalized Portmanteau Test For Independence Of Two Infinite‐Order Vector Autoregressive Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 505-544, July.
    19. Jianhua Z. Huang & Lijian Yang, 2004. "Identification of non‐linear additive autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 463-477, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Joann Jasiak & Aryan Manafi Neyazi, 2023. "GCov-Based Portmanteau Test," Papers 2312.05373, arXiv.org.

    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. Guochang Wang & Wai Keung Li & Ke Zhu, 2018. "New HSIC-based tests for independence between two stationary multivariate time series," Papers 1804.09866, arXiv.org.
    2. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    3. Bertrand Candelon & Sessi Tokpavi, 2016. "A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 240-253, April.
    4. Bertrand Candelon & Sessi Tokpavi, 2016. "A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 240-253, April.
    5. Matsui, Muneya & Mikosch, Thomas & Roozegar, Rasool & Tafakori, Laleh, 2022. "Distance covariance for random fields," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 280-322.
    6. Dette, Holger & Hildebrandt, Thimo, 2012. "A note on testing hypotheses for stationary processes in the frequency domain," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 101-114, February.
    7. Leong, Soon Heng & Urga, Giovanni, 2023. "A practical multivariate approach to testing volatility spillover," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    8. Jentsch, Carsten & Leucht, Anne & Meyer, Marco & Beering, Carina, 2016. "Empirical characteristic functions-based estimation and distance correlation for locally stationary processes," Working Papers 16-15, University of Mannheim, Department of Economics.
    9. Ahmed, Walid M.A., 2018. "On the interdependence of natural gas and stock markets under structural breaks," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 149-161.
    10. Leong, Soon Heng, 2021. "Global crude oil and the Chinese oil-intensive sectors: A comprehensive causality study," Energy Economics, Elsevier, vol. 103(C).
    11. Soylu, Pınar Kaya & Güloğlu, Bülent, 2019. "Financial contagion and flight to quality between emerging markets and U.S. bond market," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    12. Michael Eichler, 2007. "A Frequency-domain Based Test for Non-correlation between Stationary Time Series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 133-157, February.
    13. Wang, Gang-Jin & Xie, Chi & Jiang, Zhi-Qiang & Stanley, H. Eugene, 2016. "Extreme risk spillover effects in world gold markets and the global financial crisis," International Review of Economics & Finance, Elsevier, vol. 46(C), pages 55-77.
    14. Monica Billio & Lorenzo Frattarolo & Hayette Gatfaoui & Philippe de Peretti, 2016. "Clustering in Dynamic Causal Networks as a Measure of Systemic Risk on the Euro Zone," Documents de travail du Centre d'Economie de la Sorbonne 16046r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Sep 2016.
    15. Dominic Edelmann & Tobias Terzer & Donald Richards, 2021. "A Basic Treatment of the Distance Covariance," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 12-25, May.
    16. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    17. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, vol. 84(2), pages 205-231, June.
    18. Hong, Yongmiao, 2001. "A test for volatility spillover with application to exchange rates," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 183-224, July.
    19. Chafik Bouhaddioui & Roch Roy, 2004. "A Generalized Portmanteau Test for Independence of Two Infinite Order Vector Autoregressive Series," CIRANO Working Papers 2004s-06, CIRANO.
    20. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.

    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:195:y:2023:i:c:s0047259x22001427. 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.