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Joint Diagnostic Tests for Conditional Mean and Variance Specifications

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  • Juan Carlos Escanciano

    () (School of Economics and Business Administration, University of Navarra)

Abstract

This article proposes a general class of joint diagnostic tests for parametric conditional mean and variance models of possibly nonlinear and/or non-Markovian time series sequences. The new tests are based on a generalized spectral approach and, contrary to existing procedures, they do not need to choose a lag order depending on the sample size or to smooth the data. Moreover, they are robust to higher order dependence of unknown form. It turns out that the asymptotic null distributions of the new tests depend on the data generating process, so a bootstrap procedure is proposed and theoretically justified. A simulation study compares the finite sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modelling. An application to the S&P500 highlights the merits of our approach.

Suggested Citation

  • Juan Carlos Escanciano, 2006. "Joint Diagnostic Tests for Conditional Mean and Variance Specifications," Faculty Working Papers 02/06, School of Economics and Business Administration, University of Navarra.
  • Handle: RePEc:una:unccee:wp0206
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    File URL: http://www.unav.edu/documents/10174/6546776/1142591760_wp0206.pdf
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    References listed on IDEAS

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    1. 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.
    2. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
    3. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
    4. Jiti Gao & Maxwell King, 2004. "Model Specification Testing in Nonparametric and Semiparametric Time Series Econometric Models," Econometric Society 2004 North American Winter Meetings 225, Econometric Society.
    5. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    6. Chen, Xiaohong & Fan, Yanqin, 1999. "Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series," Journal of Econometrics, Elsevier, vol. 91(2), pages 373-401, August.
    7. Miguel A. Delgado & Manuel A. Dominguez & Pascal Lavergne, 2006. "Consistent Tests of Conditional Moment Restrictions," Annals of Economics and Statistics, GENES, issue 81, pages 33-67.
    8. Escanciano, J. Carlos, 2006. "Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 531-541, June.
    9. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    10. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, vol. 110(2), pages 417-435, October.
    11. Bera, Anil K & Higgins, Matthew L, 1997. "ARCH and Bilinearity as Competing Models for Nonlinear Dependence," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 43-50, January.
    12. Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
    13. Hong, Yongmiao & Lee, Tae-Hwy, 2003. "Diagnostic Checking For The Adequacy Of Nonlinear Time Series Models," Econometric Theory, Cambridge University Press, vol. 19(06), pages 1065-1121, December.
    14. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
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    Cited by:

    1. Song Xi Chen & Jiti Gao, 2010. "Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models," School of Economics Working Papers 2010-28, University of Adelaide, School of Economics.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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