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Testing non-correlation and non-causality between multivariate arma time series

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  • Marc Hallin
  • Abdessamad Saidi

Abstract

. Haugh [Journal of the American Statistical Association (1976) Vol. 71, pp. 378–85] developed an approach to the problem of testing non‐correlation (at all leads and lags) between two univariate time series. Haugh's tests however have low power against two series which are related over a long distributed lag when individual lag coefficients are relatively small. As a remedy, Koch and Yang [Journal of the American Statistical Association (1986) Vol. 8, pp. 533–44] proposed an alternative method that performs better than Haugh's under such dependencies. A multivariate extension of Haugh's procedure was proposed by El Himdi and Roy [The Canadian Journal of Statistics (1997) Vol. 25, pp. 233–56], but suffers the same weaknesses as the original univariate method. We develop here an asymptotic test generalizing Koch and Yang's method to the multivariate case. Our method includes El Himdi and Roy's as a special case. Based on the same idea, we also suggest a generalization of the El Himdi and Roy procedure for testing causality in the sense of Granger [Econometrica (1969) Vol. 37, pp. 424–38] between two multivariate series. A Monte Carlo study is conducted, which indicates that our approach performs better than El Himdi and Roy's for a wide range of models. Both procedures are applied to the problem of testing the absence of correlation between Canadian and US economic indicators, and to a brief study of causality between money and income in Canada.
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Suggested Citation

  • Marc Hallin & Abdessamad Saidi, 2005. "Testing non-correlation and non-causality between multivariate arma time series," ULB Institutional Repository 2013/127945, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/127945
    Note: SCOPUS: ar.j
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    References listed on IDEAS

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    1. Franklin Satterthwaite, 1941. "Synthesis of variance," Psychometrika, Springer;The Psychometric Society, vol. 6(5), pages 309-316, October.
    2. Boudjellaba, Hafida & Dufour, Jean-Marie & Roy, Roch, 1994. "Simplified conditions for noncausality between vectors in multivariate ARMA models," Journal of Econometrics, Elsevier, vol. 63(1), pages 271-287, July.
    3. Pierce, David A. & Haugh, Larry D., 1977. "Causality in temporal systems : Characterization and a survey," Journal of Econometrics, Elsevier, vol. 5(3), pages 265-293, May.
    4. Larry D. Haugh & David A. Pierce, 1977. "Causality in temporal systems: characterizations and a survey," Special Studies Papers 87, Board of Governors of the Federal Reserve System (U.S.).
    5. Osborn, Denise R, 1984. "Causality Testing and Its Implications for Dynamic Econometric Models," Economic Journal, Royal Economic Society, vol. 94(376a), pages 82-96, Supplemen.
    6. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
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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. Bouhaddioui, Chafik & Roy, Roch, 2006. "On the distribution of the residual cross-correlations of infinite order vector autoregressive series and applications," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 58-68, January.
    4. Chafik Bouhaddioui & Roch Roy, 2004. "A Generalized Portmanteau Test for Independence of Two Infinite Order Vector Autoregressive Series," CIRANO Working Papers 2004s-06, CIRANO.
    5. 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.
    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. Chafik Bouhaddioui & Roch Roy, 2003. "On the Distribution of the Residual Cross-Correlations between Two Uncorrelated Infinite Order Vector Autoregressive Series," CIRANO Working Papers 2003s-41, CIRANO.
    8. 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.
    9. Aleksandra Grzesiek & Prashant Giri & S. Sundar & Agnieszka WyŁomańska, 2020. "Measures of Cross‐Dependence for Bidimensional Periodic AR(1) Model with α‐Stable Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 785-807, November.
    10. 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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