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On portmanteau-type tests for nonlinear multivariate time series

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  • De Gooijer, Jan G.

Abstract

A general framework to devise portmanteau-type test statistics for a general class of multivariate nonlinear time series models with vector martingale difference errors is formulated. Based on this framework a suite of individual and mixed multivariate test statistics is considered. Two applications are developed: single- and multiple-lag test statistics. In each case, the resulting portmanteau test statistic is based on multivariate residuals and multivariate squared residuals. Moreover, single- and multiple-lag mixed multivariate portmanteau-type tests are introduced. These test statistics are designed to detect different forms of inadequacies in the model residuals jointly. All proposed tests take uncertainty due to model estimation properly into account. The asymptotic null distribution of each test statistic follows from the asymptotic distribution of the general portmanteau-type test statistic in a natural way. Some considerations are given to the empirical size and power of six test statistics via a simulation study. All tests have satisfactory size and power properties in finite samples. To demonstrate their practical use, the proposed test statistics are applied to the residuals of a vector bivariate nonlinear threshold model fitted to U.S. interest rates.

Suggested Citation

  • De Gooijer, Jan G., 2023. "On portmanteau-type tests for nonlinear multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:jmvana:v:195:y:2023:i:c:s0047259x23000039
    DOI: 10.1016/j.jmva.2023.105157
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    References listed on IDEAS

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    1. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
    2. Christian Francq & Hamdi Raïssi, 2007. "Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 454-470, May.
    3. H. Wong & W. Li, 2002. "Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 45-59, March.
    4. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    5. Guochang Wang & Ke Zhu & Xiaofeng Shao, 2022. "Testing for the Martingale Difference Hypothesis in Multivariate Time Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 980-994, June.
    6. 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.
    7. Jan G. De Gooijer & Ao Yuan, 2016. "Non parametric portmanteau tests for detecting non linearities in high dimensions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 385-399, January.
    8. Chabot-Hallé, Dominique & Duchesne, Pierre, 2008. "Diagnostic checking of multivariate nonlinear time series models with martingale difference errors," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 997-1005, June.
    9. Esam Mahdi & A. Ian McLeod, 2012. "Improved multivariate portmanteau test," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 211-222, March.
    10. Guodong Li & Wai Keung Li, 2005. "Diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach," Biometrika, Biometrika Trust, vol. 92(3), pages 691-701, September.
    11. Ke. Zhu, 2013. "A mixed portmanteau test for ARMA-GARCH models by the quasi-maximum exponential likelihood estimation approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 230-237, March.
    12. Heung Wong & Shiqing Ling, 2005. "Mixed Portmanteau Tests for Time‐Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 569-579, July.
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