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Testing for Time-Varying Properties Under Misspecified Conditional Mean and Variance

Author

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  • Daiki Maki

    (Doshisha University)

  • Yasushi Ota

    (Okayama University of Science)

Abstract

This study examines statistical performance of tests for time-varying properties under misspecified conditional mean and variance. When time-varying properties of the conditional mean are tested in the case in which data have no time-varying mean but have time-varying variance, asymptotic tests have size distortions. The distortions are minimized by the use of a bootstrap method. Similarly, when time-varying properties of the conditional variance are tested in the case in which data have time-varying mean but no time-varying variance, asymptotic tests have large size distortions. The distortions are not improved even by the use of bootstrap methods. We show that tests for time-varying properties of the conditional mean by the bootstrap are robust regardless of the time-varying variance model, whereas tests for time-varying properties of the conditional variance do not perform well in the presence of misspecified time-varying mean.

Suggested Citation

  • Daiki Maki & Yasushi Ota, 2021. "Testing for Time-Varying Properties Under Misspecified Conditional Mean and Variance," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1167-1182, April.
    • Handle: RePEc:kap:compec:v:57:y:2021:i:4:d:10.1007_s10614-020-10014-4
    DOI: 10.1007/s10614-020-10014-4
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    1. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
    2. Zhou Zhou, 2013. "Heteroscedasticity and Autocorrelation Robust Structural Change Detection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 726-740, June.
    3. Lumsdaine, Robin L. & Ng, Serena, 1999. "Testing for ARCH in the presence of a possibly misspecified conditional mean," Journal of Econometrics, Elsevier, vol. 93(2), pages 257-279, December.
    4. Boldea, Otilia & Cornea-Madeira, Adriana & Hall, Alastair R., 2019. "Bootstrapping structural change tests," Journal of Econometrics, Elsevier, vol. 213(2), pages 359-397.
    5. Pierre Perron & Yohei Yamamoto, 2019. "Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model," Econometrics, MDPI, vol. 7(2), pages 1-11, May.
    6. Jean-Yves Pitarakis, 2004. "Least squares estimation and tests of breaks in mean and variance under misspecification," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 32-54, June.
    7. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    8. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    9. Lundbergh, Stefan & Terasvirta, Timo & van Dijk, Dick, 2003. "Time-Varying Smooth Transition Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 104-121, January.
    10. Van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for Smooth Transition Nonlinearity in the Presence of Outliers," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(2), pages 217-235, April.
    11. Blake, Andrew P. & Kapetanios, George, 2007. "Testing for ARCH in the presence of nonlinearity of unknown form in the conditional mean," Journal of Econometrics, Elsevier, vol. 137(2), pages 472-488, April.
    12. Matthew T. Holt & Joseph V. Balagtas, 2009. "Estimating Structural Change with Smooth Transition Regressions: An Application to Meat Demand," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(5), pages 1424-1431.
    13. Catani, P.S. & Ahlgren, N.J.C., 2017. "Combined Lagrange multiplier test for ARCH in vector autoregressive models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 62-84.
    14. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    15. Stan Hurn & Ralf Becker, 2009. "Testing for Nonlinearity in Mean in the Presence of Heteroskedasticity," Economic Analysis and Policy, Elsevier, vol. 39(2), pages 311-326, September.
    16. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    17. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    18. Pavlidis Efthymios G & Paya Ivan & Peel David A, 2010. "Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(3), pages 1-40, May.
    19. Pavlidis Efthymios G. & Paya Ivan & Peel David A., 2013. "Nonlinear causality tests and multivariate conditional heteroskedasticity: a simulation study," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(3), pages 297-312, May.
    20. Kim, Kun Ho & Kim, Taejin, 2016. "Capital asset pricing model: A time-varying volatility approach," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 268-281.
    21. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
    22. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
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