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Tests for non‐correlation of two cointegrated ARMA time series

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  • DINH TUAN PHAM
  • ROCH ROY
  • LYNE CÉDRAS

Abstract

In multivariate time series modelling, we are often led to investigate the existence of a relationship between two time series. Here, we generalize the procedure proposed by Haugh (1976) and extended by El Himdi and Roy (1997) for multivariate stationary ARMA time series to the case of cointegrated (or partially nonstationary) ARMA series. The main contribution consists in showing that, in the case of two uncorrelated cointegrated time series, an arbitrary vector of residual cross‐correlation matrices asymptotically follows the same distribution as the corresponding vector of cross‐correlation matrices between the two innovation series. The estimation method from which the residuals are obtained can be the conditional maximum likelihood method as discussed in Yap and Reinsel (1995) or some other which has the same convergence rate. From this result, it follows that the considered test statistics, which are based on residual cross‐correlation matrices, asymptotically follow χ2 distributions. The finite sample properties, under the null hypothesis, of the test statistics are studied by simulation.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:5:p:553-577
    DOI: 10.1111/1467-9892.00322
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    References listed on IDEAS

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    1. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(1), pages 1-27, March.
    2. Marc Hallin & Jana Jureckova & Jan Picek & Toufik Zahaf, 1999. "Nonparametric tests of independence of two autoregressive time series based on autoregression rank scores," ULB Institutional Repository 2013/127942, ULB -- Universite Libre de Bruxelles.
    3. Marc Hallin & Jana Jureckova & Jan Picek & Toufik Zahaf, 1999. "Nonparametric tests of independence between two autoregressive series based on autoregression rank scores," ULB Institutional Repository 2013/2081, ULB -- Universite Libre de Bruxelles.
    4. Hatanaka, Michio, 1996. "Time-Series-Based Econometrics: Unit Roots and Co-integrations," OUP Catalogue, Oxford University Press, number 9780198773535.
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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. Melard, Guy & Roy, Roch & Saidi, Abdessamad, 2006. "Exact maximum likelihood estimation of structured or unit root multivariate time series models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2958-2986, July.
    3. 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 16046, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. Pierre Duchesne, 2005. "Testing for serial correlation of unknown form in cointegrated time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 575-595, September.
    5. Chafik Bouhaddioui & Roch Roy, 2004. "A Generalized Portmanteau Test for Independence of Two Infinite Order Vector Autoregressive Series," CIRANO Working Papers 2004s-06, CIRANO.
    6. Mariano Matilla‐García & José Miguel Rodríguez & Manuel Ruiz Marín, 2010. "A symbolic test for testing independence between time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 76-85, March.

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