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Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models

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  • Bal'azs Csan'ad Cs'aji

Abstract

A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here, we suggest a finite sample approach, called ScoPe, to construct distribution-free confidence regions around the QML estimate, which have exact coverage probabilities, despite no additional assumptions about moments are made. ScoPe is inspired by the recently developed Sign-Perturbed Sums (SPS) method, which however cannot be applied in the GARCH case. ScoPe works by perturbing the score function using randomly permuted residuals. This produces alternative samples which lead to exact confidence regions. Experiments on simulated and stock market data are also presented, and ScoPe is compared with the asymptotic theory and bootstrap approaches.

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  • 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.
    • Handle: RePEc:arx:papers:1807.08390
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    1. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    2. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    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. 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.
    5. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
    6. 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.
    7. László Gerencsér & Zsanett Orlovits, 2012. "Real time estimation of stochastic volatility processes," Annals of Operations Research, Springer, vol. 200(1), pages 223-246, November.
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