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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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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 56 (2012)
Issue (Month): 11 ()
Pages: 3198-3211

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Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3198-3211

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Web page: http://www.elsevier.com/locate/csda

Related research

Keywords: Conditional heteroskedasticity; Heavy tails; Weak identification; Parametric bootstrap; Monte Carlo p-value; Projection technique;

References

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  1. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  2. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  3. Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
  4. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
  5. Jun Ma & Charles Nelson & Richard Startz, 2007. "Spurious Inference in the GARCH(1,1) Model When It Is Weakly Identified," Working Papers UWEC-2006-14-P, University of Washington, Department of Economics, revised Mar 2007.
  6. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  7. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
  8. Jean-Marie Dufour & Mohamed Taamouti, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," CIRANO Working Papers 2003s-39, CIRANO.
  9. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  10. Francq, Christian & Zakoian, Jean-Michel, 2007. "Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1265-1284, September.
  11. Touhami Abdelkhalek & Jean-Marie Dufour, 1998. "Statistical Inference For Computable General Equilibrium Models, With Application To A Model Of The Moroccan Economy," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 520-534, November.
  12. 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 705-30, August.
  13. DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 03-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  14. Elise Coudin & Jean-Marie Dufour, 2009. "Finite-sample distribution-free inference in linear median regressions under heteroscedasticity and non-linear dependence of unknown form," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages S19-S49, 01.
  15. 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.
  16. Bolduc, Denis & Khalaf, Lynda & Yélou, Clément, 2010. "Identification robust confidence set methods for inference on parameter ratios with application to discrete choice models," Journal of Econometrics, Elsevier, vol. 157(2), pages 317-327, August.
  17. Dufour, Jean-Marie & Valéry, Pascale, 2009. "Exact and asymptotic tests for possibly non-regular hypotheses on stochastic volatility models," Journal of Econometrics, Elsevier, vol. 150(2), pages 193-206, June.
  18. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  19. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  20. 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.
  21. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
  22. Dufour, Jean-Marie & Jouini, Tarek, 2006. "Finite-sample simulation-based inference in VAR models with application to Granger causality testing," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 229-254.
  23. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  24. Dufour, J.-M., 1986. "Nonlinear hypotheses, inequality restrictions and non-nested hypotheses: Exact simultaneous tests in linear regressions," CORE Discussion Papers 1986016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  25. Søren Tolver Jensen & Anders Rahbek, 2004. "Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case," Econometrica, Econometric Society, vol. 72(2), pages 641-646, 03.
  26. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-43, August.
  27. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  28. Asger Lunde & Peter Reinhard Hansen, 2001. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?," Working Papers 2001-04, Brown University, Department of Economics.
  29. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2010. "On the precision of Calvo parameter estimates in structural NKPC models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1582-1595, September.
  30. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
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Cited by:
  1. Ghoudi, Kilani & Rémillard, Bruno, 2014. "Comparison of specification tests for GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 291-300.

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