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New HSIC-based tests for independence between two stationary multivariate time series

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  • Guochang Wang
  • Wai Keung Li
  • Ke Zhu

Abstract

This paper proposes some novel one-sided omnibus tests for independence between two multivariate stationary time series. These new tests apply the Hilbert-Schmidt independence criterion (HSIC) to test the independence between the innovations of both time series. Under regular conditions, the limiting null distributions of our HSIC-based tests are established. Next, our HSIC-based tests are shown to be consistent. Moreover, a residual bootstrap method is used to obtain the critical values for our HSIC-based tests, and its validity is justified. Compared with the existing cross-correlation-based tests for linear dependence, our tests examine the general (including both linear and non-linear) dependence to give investigators more complete information on the causal relationship between two multivariate time series. The merits of our tests are illustrated by some simulation results and a real example.

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  • 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.
    • Handle: RePEc:arx:papers:1804.09866
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    1. 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.
    2. Hallin, Marc & Saidi, Abdessamad, 2007. "Optimal Tests of Noncorrelation Between Multivariate Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 938-951, September.
    3. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    4. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    5. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
    6. Lee, Tae-Hwy & Long, Xiangdong, 2009. "Copula-based multivariate GARCH model with uncorrelated dependent errors," Journal of Econometrics, Elsevier, vol. 150(2), pages 207-218, June.
    7. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    8. Cees Diks & Marcin Wolski, 2016. "Nonlinear Granger Causality: Guidelines for Multivariate Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1333-1351, November.
    9. Shao, Xiaofeng, 2009. "A Generalized Portmanteau Test For Independence Between Two Stationary Time Series," Econometric Theory, Cambridge University Press, vol. 25(1), pages 195-210, February.
    10. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    11. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.
    12. Abhay Abhyankar, Bing Xu, and Jiayue Wang, 2013. "Oil Price Shocks and the Stock Market: Evidence from Japan," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    13. repec:ulb:ulbeco:2013/2129 is not listed on IDEAS
    14. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    15. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
    16. Escanciano, J. Carlos, 2006. "Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 531-541, June.
    17. 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.
    18. Hong, Yongmiao, 1996. "Testing for independence between two covariance stationary time series," MPRA Paper 108731, University Library of Munich, Germany.
    19. 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.
    20. Shiqing Ling & W. K. Li, 1997. "Diagnostic checking of nonlinear multivariate time series with multivariate arch errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 447-464, September.
    21. 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.
    22. A. Sen & B. Sen, 2014. "Testing independence and goodness-of-fit in linear models," Biometrika, Biometrika Trust, vol. 101(4), pages 927-942.
    23. William Schwert, G., 1979. "Tests of causality : The message in the innovations," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 10(1), pages 55-96, January.
    24. Choudhry, Taufiq & Papadimitriou, Fotios I. & Shabi, Sarosh, 2016. "Stock market volatility and business cycle: Evidence from linear and nonlinear causality tests," Journal of Banking & Finance, Elsevier, vol. 66(C), pages 89-101.
    25. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    26. Y. K. Tse, 2002. "Residual-based diagnostics for conditional heteroscedasticity models," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 358-374, June.
    27. Dinh Tuan Pham & Roch Roy & Lyne Cédras, 2003. "Tests for non‐correlation of two cointegrated ARMA time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 553-577, September.
    28. Wang, Yudong & Wu, Chongfeng & Yang, Li, 2013. "Oil price shocks and stock market activities: Evidence from oil-importing and oil-exporting countries," Journal of Comparative Economics, Elsevier, vol. 41(4), pages 1220-1239.
    29. 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.
    30. Hiemstra, Craig & Jones, Jonathan D, 1994. "Testing for Linear and Nonlinear Granger Causality in the Stock Price-Volume Relation," Journal of Finance, American Finance Association, vol. 49(5), pages 1639-1664, December.
    31. Brunner, Karl & Meltzer, Allan H., 1979. "Three aspects of policy and policymaking: Knowledge, data and institutions," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 10(1), pages 1-7, January.
    32. 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.
    33. 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.
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    Cited by:

    1. Wan, Phyllis & Davis, Richard A., 2022. "Goodness-of-fit testing for time series models via distance covariance," Journal of Econometrics, Elsevier, vol. 227(1), pages 4-24.

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