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Testing constancy of unconditional variance in volatility models by misspecification and specification tests

Author

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  • Annastiina Silvennoinen

    (QUT)

  • Timo Terasvirta

    (CREATES)

Abstract

The topic of this paper is testing the hypothesis of constant unconditional variance in GARCH models against the alternative that the unconditional variance changes deterministically over time. Tests of this hypothesis have previously been performed as misspecification tests after fitting a GARCH model to the original series. It is found by simulation that the positive size distortion present in these tests is a function of the kurtosis of the GARCH process. Adjusting the size by numerical methods is considered. The possibility of testing the constancy of the unconditional variance before fitting a GARCH model to the data is discussed. The power of the ensuing test is vastly superior to that of the misspecification test and the size distortion minimal. The test has reasonable power already in very short time series. It would thus serve as a test of constant variance in conditional mean models. An application to exchange rate returns is included.

Suggested Citation

  • Annastiina Silvennoinen & Timo Terasvirta, 2015. "Testing constancy of unconditional variance in volatility models by misspecification and specification tests," NCER Working Paper Series 108, National Centre for Econometric Research.
    • Handle: RePEc:qut:auncer:2015_06
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    File URL: http://www.ncer.edu.au/papers/documents/WP108.pdf
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    References listed on IDEAS

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    Cited by:

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    2. Cristina Amado & Annastiina Silvennoinen & Timo Terasvirta, 2017. "Modelling and Forecasting WIG20 Daily Returns," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(3), pages 173-200, September.
    3. He, Changli & Kang, Jian & Teräsvirta, Timo & Zhang, Shuhua, 2019. "The shifting seasonal mean autoregressive model and seasonality in the Central England monthly temperature series, 1772–2016," Econometrics and Statistics, Elsevier, vol. 12(C), pages 1-24.
    4. Fonseca, Thais C O & Cerqueira, Vinicius S & Migon, Helio S & Torres, Christian A C, 2021. "Evaluating the performance of degrees of freedom estimation in asymmetric GARCH models with t-student innovations," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 40(2), April.
    5. Christian Conrad & Melanie Schienle, 2020. "Testing for an Omitted Multiplicative Long-Term Component in GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 229-242, April.
    6. Pape, Katharina & Wied, Dominik & Galeano, Pedro, 2016. "Monitoring multivariate variance changes," Journal of Empirical Finance, Elsevier, vol. 39(PA), pages 54-68.
    7. Annastiina Silvennoinen & Timo Teräsvirta, 2017. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," CREATES Research Papers 2017-28, Department of Economics and Business Economics, Aarhus University.
    8. Anthony D. Hall & Annastiina Silvennoinen & Timo Teräsvirta, 2021. "Four Australian Banks and the Multivariate Time-Varying Smooth Transition Correlation GARCH model," CREATES Research Papers 2021-13, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    Keywords

    autoregressive conditional heteroskedasticity; modelling volatility; testing parameter constancy; time-varying GARCH;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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