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Bootstrapping multivariate portmanteau tests for vector autoregressive models with weak assumptions on errors

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  • Li, Muyi
  • Zhang, Yanfen

Abstract

This article discusses diagnostic checking for vector autoregressive models with uncorrelated but not independent innovations. In this situation, the multivariate portmanteau tests are severely over-sized due to the misspecification of critical values obtained from the χ2 distribution. To address this issue, a random weighting bootstrap procedure is proposed to approximate the null distribution when the error is assumed to be martingale difference sequence. When this assumption is violated, a blockwise random weighting is further applied to replicate the dependence structure of innovations. The first-order asymptotic validity of these bootstrap procedures is derived. Monte Carlo experiments under various scenarios suggest the effectiveness of the random weighting bootstrap approaches in comparison with existing approaches. Finally, the proposed testing procedure is illustrated in an application to analyze feedback dynamics between the real GNP growth and the unemployment rate in the US.

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  • Li, Muyi & Zhang, Yanfen, 2022. "Bootstrapping multivariate portmanteau tests for vector autoregressive models with weak assumptions on errors," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:csdana:v:165:y:2022:i:c:s0167947321001559
    DOI: 10.1016/j.csda.2021.107321
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    1. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 158(1), pages 7-24, September.
    2. Duchesne, Pierre & Lafaye De Micheaux, Pierre, 2010. "Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 858-862, April.
    3. 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.
    4. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    5. Ke Zhu, 2016. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 463-485, March.
    6. Juan Carlos Escanciano & Ignacio N. Lobato & Lin Zhu, 2013. "Automatic Specification Testing for Vector Autoregressions and Multivariate Nonlinear Time Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 426-437, October.
    7. Guodong Li & Chenlei Leng & Chih-Ling Tsai, 2014. "A Hybrid Bootstrap Approach To Unit Root Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 299-321, July.
    8. Guo, Shaojun & Li, Dong & Li, Muyi, 2019. "Strict stationarity testing and GLAD estimation of double autoregressive models," Journal of Econometrics, Elsevier, vol. 211(2), pages 319-337.
    9. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    10. Jinyuan Chang & Qiwei Yao & Wen Zhou, 2017. "Testing for high-dimensional white noise using maximum cross-correlations," Biometrika, Biometrika Trust, vol. 104(1), pages 111-127.
    11. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    12. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    13. 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.
    14. Hill, Jonathan B. & Motegi, Kaiji, 2019. "Testing the white noise hypothesis of stock returns," Economic Modelling, Elsevier, vol. 76(C), pages 231-242.
    15. Zhu, Ke & Li, Wai Keung, 2015. "A bootstrapped spectral test for adequacy in weak ARMA models," Journal of Econometrics, Elsevier, vol. 187(1), pages 113-130.
    16. Lobato, I.N. & Nankervis, John C. & Savin, N.E., 2002. "Testing For Zero Autocorrelation In The Presence Of Statistical Dependence," Econometric Theory, Cambridge University Press, vol. 18(3), pages 730-743, June.
    17. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
    18. Shiqing Ling & Ruey S. Tsay & Yaxing Yang, 2021. "Testing Serial Correlation and ARCH Effect of High-Dimensional Time-Series Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 136-147, January.
    19. Chang, Jinyuan & Yao, Qiwei & Zhou, Wen, 2017. "Testing for high-dimensional white noise using maximum cross-correlations," LSE Research Online Documents on Economics 68531, London School of Economics and Political Science, LSE Library.
    20. Smeekes, S. & Urbain, J.R.Y.J., 2014. "A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing," Research Memorandum 008, Maastricht University, Graduate School of Business and Economics (GSBE).
    21. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
    22. Shao, Xiaofeng, 2011. "A bootstrap-assisted spectral test of white noise under unknown dependence," Journal of Econometrics, Elsevier, vol. 162(2), pages 213-224, June.
    23. Y. Boubacar Maïnassara, 2012. "Selection of weak VARMA models by modified Akaike's information criteria," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 121-130, January.
    24. Evans, George W, 1989. "Output and Unemployment Dynamics in the United States: 1950-1985," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(3), pages 213-237, July-Sept.
    25. Tsay, Ruey S., 2020. "Testing serial correlations in high-dimensional time series via extreme value theory," Journal of Econometrics, Elsevier, vol. 216(1), pages 106-117.
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