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A Bootstrap Test for the Existence of Moments for GARCH Processes

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  • Alexander Heinemann

Abstract

This paper studies the joint inference on conditional volatility parameters and the innovation moments by means of bootstrap to test for the existence of moments for GARCH(p,q) processes. We propose a residual bootstrap to mimic the joint distribution of the quasi-maximum likelihood estimators and the empirical moments of the residuals and also prove its validity. A bootstrap-based test for the existence of moments is proposed, which provides asymptotically correctly-sized tests without losing its consistency property. It is simple to implement and extends to other GARCH-type settings. A simulation study demonstrates the test's size and power properties in finite samples and an empirical application illustrates the testing approach.

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  • Alexander Heinemann, 2019. "A Bootstrap Test for the Existence of Moments for GARCH Processes," Papers 1902.01808, arXiv.org, revised Jul 2019.
    • Handle: RePEc:arx:papers:1902.01808
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    References listed on IDEAS

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    1. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    2. Giuseppe Cavaliere & Rasmus Søndergaard Pedersen & Anders Rahbek, 2018. "The Fixed Volatility Bootstrap for a Class of Arch(q) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 920-941, November.
    3. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    4. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    5. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    6. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    7. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
    8. Alexander Heinemann & Sean Telg, 2018. "A Residual Bootstrap for Conditional Expected Shortfall," Papers 1811.11557, arXiv.org.
    9. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    10. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    11. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    12. Corradi, Valentina & Iglesias, Emma M., 2008. "Bootstrap refinements for QML estimators of the GARCH(1,1) parameters," Journal of Econometrics, Elsevier, vol. 144(2), pages 500-510, June.
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    Cited by:

    1. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.
    2. Francq, Christian & Zakoian, Jean-Michel, 2021. "Testing the existence of moments and estimating the tail index of augmented garch processes," MPRA Paper 110511, University Library of Munich, Germany.
    3. Francq, Christian & Zakoian, Jean-Michel, 2024. "Finite moments testing in a general class of nonlinear time series models," MPRA Paper 121193, University Library of Munich, Germany.

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