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Corrected portmanteau tests for VAR models with time-varying variance

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  • Patilea, V.
  • Raïssi, H.

Abstract

The problem of test of fit for Vector AutoRegressive (VAR) processes with unconditionally heteroscedastic errors is studied. This problem is motivated by numerous examples of series presenting such a pattern. Our analysis is based on the residual autocorrelations obtained from Ordinary Least Squares (OLS), Generalized Least Squares (GLS) and Adaptive Least Squares (ALS) estimation of the autoregressive parameters. The GLS approach requires the knowledge of the variance structure while the ALS method is adapted to the unknown time-varying unconditional covariance which is estimated by kernel smoothing. It is shown that the ALS and GLS residual autocorrelations are asymptotically equivalent. It is also found that the asymptotic distribution of the OLS residual autocorrelations can be quite different from the standard chi-square asymptotic distribution obtained in a correctly specified VAR model with i.i.d. innovations. As a consequence the standard portmanteau tests which are available in routinely used software are unreliable in our framework. Using our results modified portmanteau tests based on the OLS and ALS residual autocorrelations and which take into account time varying covariance are proposed. The finite sample properties of the goodness-of-fit tests we consider are investigated by Monte Carlo experiments. The theoretical results are also illustrated using a U.S. economic data set.

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  • Patilea, V. & Raïssi, H., 2013. "Corrected portmanteau tests for VAR models with time-varying variance," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 190-207.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:190-207
    DOI: 10.1016/j.jmva.2012.12.004
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    3. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    4. Bibi Cai & Enwen Zhu & Shiqing Ling, 2024. "Asymptotic inference of the ARMA model with time‐functional variance noises," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1230-1258, September.
    5. Valentin Patilea & Hamdi Raïssi, 2014. "Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1099-1111, September.
    6. Quentin Giai Gianetto & Hamdi Raïssi, 2015. "Testing Instantaneous Causality in Presence of Nonconstant Unconditional Covariance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 46-53, January.
    7. Raïssi, Hamdi, 2018. "Testing normality for unconditionally heteroscedastic macroeconomic variables," Economic Modelling, Elsevier, vol. 70(C), pages 140-146.
    8. Hamdi Raissi, 2022. "On the dependence structure of the trade/no trade sequence of illiquid assets," Papers 2203.08223, arXiv.org.

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