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Automatic Specification Testing for Vector Autoregressions and Multivariate Nonlinear Time Series Models


  • Juan Carlos Escanciano
  • Ignacio N. Lobato
  • Lin Zhu


This article introduces an automatic test for the correct specification of a vector autoregression (VAR) model. The proposed test statistic is a Portmanteau statistic with an automatic selection of the order of the residual serial correlation tested. The test presents several attractive characteristics: simplicity, robustness, and high power in finite samples. The test is simple to implement since the researcher does not need to specify the order of the autocorrelation tested and the proposed critical values are simple to approximate, without resorting to bootstrap procedures. In addition, the test is robust to the presence of conditional heteroscedasticity of unknown form and accounts for estimation uncertainty without requiring the computation of large-dimensional inverses of near-to-singularity covariance matrices. The basic methodology is extended to general nonlinear multivariate time series models. Simulations show that the proposed test presents higher power than the existing ones for models commonly employed in empirical macroeconomics and empirical finance. Finally, the test is applied to the classical bivariate VAR model for GNP (gross national product) and unemployment of Blanchard and Quah (1989) and Evans (1989). Online supplementary material includes proofs and additional details.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlbes:v:31:y:2013:i:4:p:426-437
    DOI: 10.1080/07350015.2013.803973

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    Cited by:

    1. Pedro H. C. Sant’Anna, 2017. "Testing for Uncorrelated Residuals in Dynamic Count Models With an Application to Corporate Bankruptcy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 349-358, July.
    2. 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.

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