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A Generalized Portmanteau Test For Independence Of Two Infinite‐Order Vector Autoregressive Series

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  • Chafik Bouhaddioui
  • Roch Roy

Abstract

. In many situations, we want to verify the existence of a relationship between multivariate time series. Here, we propose a semiparametric approach for testing the independence between two infinite‐order vector autoregressive (VAR(∞)) series, which is an extension of Hong's [Biometrika (1996c) vol. 83, 615–625] univariate results. We first filter each series by a finite‐order autoregression and the test statistic is a standardized version of a weighted sum of quadratic forms in the residual cross‐correlation matrices at all possible lags. The weights depend on a kernel function and on a truncation parameter. Using a result of Lewis and Reinsel [Journal of Multivariate Analysis (1985) Vol. 16, pp. 393–411], the asymptotic distribution of the test statistic is derived under the null hypothesis and its consistency is also established for a fixed alternative of serial cross‐correlation of unknown form. Apart from standardization factors, the multivariate portmanteau statistic proposed by Bouhaddioui and Roy [Statistics and Probability Letters (2006) vol. 76, pp. 58–68] that takes into account a fixed number of lags can be viewed as a special case by using the truncated uniform kernel. However, many kernels lead to a greater power, as shown in an asymptotic power analysis and by a small simulation study in finite samples. A numerical example with real data is also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:4:p:505-544
    DOI: 10.1111/j.1467-9892.2006.00473.x
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    References listed on IDEAS

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    1. Hong, Yongmiao, 1996. "Testing for independence between two covariance stationary time series," MPRA Paper 108731, University Library of Munich, Germany.
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    Cited by:

    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. 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.
    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. Mayer, Alexander, 2020. "(Consistently) testing strict exogeneity against the alternative of predeterminedness in linear time-series models," Economics Letters, Elsevier, vol. 193(C).
    6. 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).
    7. 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.
    8. Simos G. Meintanis & Joseph Ngatchou-Wandji & James Allison, 2018. "Testing for serial independence in vector autoregressive models," Statistical Papers, Springer, vol. 59(4), pages 1379-1410, December.
    9. 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.
    10. Leong, Soon Heng & Urga, Giovanni, 2023. "A practical multivariate approach to testing volatility spillover," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    11. Chu, Ba, 2023. "A distance-based test of independence between two multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).

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