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Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations

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  • Luger, Richard

Abstract

A general method is proposed for the construction of valid simultaneous confidence sets in the context of stationary GARCH models. The proposed method proceeds by numerically inverting the conventional likelihood ratio test. In order to hedge against the risk of a spurious rejection, candidate points that are rejected by the conventional test undergo a finite-sample parametric bootstrap test. A projection technique is then exploited to produce conservative confidence sets for general functions of the parameters. A simulation study illustrates the performance of the parametric bootstrap approach in the context of a GARCH model with heavy-tailed and skewed innovations. That model is then used in an empirical application to construct simultaneous confidence intervals for multi-step ahead volatility forecasts for the returns on a major stock market index.

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  • Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3198-3211
    DOI: 10.1016/j.csda.2011.08.008
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    2. Fernanda Maria Müller & Fábio M Bayer, 2017. "Improved two-component tests in Beta-Skew-t-EGARCH models," Economics Bulletin, AccessEcon, vol. 37(4), pages 2364-2373.
    3. Bernardina Algieri & Arturo Leccadito & Pietro Toscano, 2021. "A Time-Varying Gerber Statistic: Application of a Novel Correlation Metric to Commodity Price Co-Movements," Forecasting, MDPI, vol. 3(2), pages 1-16, May.
    4. Szczygielski, Jan Jakub & Brzeszczyński, Janusz & Charteris, Ailie & Bwanya, Princess Rutendo, 2022. "The COVID-19 storm and the energy sector: The impact and role of uncertainty," Energy Economics, Elsevier, vol. 109(C).
    5. Bal'azs Csan'ad Cs'aji, 2018. "Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models," Papers 1807.08390, arXiv.org.
    6. Ghoudi, Kilani & Rémillard, Bruno, 2014. "Comparison of specification tests for GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 291-300.
    7. Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.

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