Estimation of tail thickness parameters from GJR-GARCH models
We propose a method of estimating the Pareto tail thickness parameter of the unconditional distribution of a financial time series by exploiting the implications of a GJR-GARCH volatility model. The method is based on some recent work on the extremes of GARCH-type processes and extends the method proposed by Berkes, Horváth and Kokoszka (2003). We show that the estimator of tail thickness is consistent and converges at rate √T to a normal distribution (where T is the sample size), provided the model for conditional variance is correctly specified as a GJR-GARCH. This is much faster than the convergence rate of the Hill estimator, since that procedure only uses a vanishing fraction of the sample. We also develop new specification tests based on this method and propose new alternative estimates of unconditional value at risk. We show in Monte Carlo simulations the advantages of our procedure in finite samples; and finally an application concludes the paper
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- Niklas Wagner & Terry A. Marsh, 2004. "Measuring Tail Thickness under GARCH and an Application to Extreme Exchange Rate Changes," Econometrics 0401008, EconWPA.
- 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.
- Andrews, Donald W K, 1991.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Econometric Society, vol. 59(3), pages 817-58, May.
- Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Benoit Mandelbrot, 1963.
"The Variation of Certain Speculative Prices,"
The Journal of Business,
University of Chicago Press, vol. 36, pages 394.
- Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
- Jansen, Dennis W & de Vries, Casper G, 1991.
"On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective,"
The Review of Economics and Statistics,
MIT Press, vol. 73(1), pages 18-24, February.
- Dennis W. Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers 1989-006, Federal Reserve Bank of St. Louis.
- Hill, Jonathan B., 2010.
"On Tail Index Estimation For Dependent, Heterogeneous Data,"
Cambridge University Press, vol. 26(05), pages 1398-1436, October.
- Jonathan B. Hill, 2005. "On Tail Index Estimation for Dependent, Heterogenous Data," Econometrics 0505005, EconWPA, revised 27 May 2005.
- Andrews, Donald W K, 1987. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers [On Unification of the Asymptotic Theory of Nonlinear Econometric Models]," Econometrica, Econometric Society, vol. 55(6), pages 1465-71, November.
- Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-16, April.
- Groenendijk, Patrick A. & Lucas, Andre & de Vries, Casper G., 1995. "A note on the relationship between GARCH and symmetric stable processes," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 253-264, September.
- Linton, Oliver, 1993.
"Adaptive Estimation in ARCH Models,"
Cambridge University Press, vol. 9(04), pages 539-569, August.
- Ling, Shiqing & McAleer, Michael, 2003.
"Asymptotic Theory For A Vector Arma-Garch Model,"
Cambridge University Press, vol. 19(02), pages 280-310, April.
- Markowitz, Harry M, 1991.
" Foundations of Portfolio Theory,"
Journal of Finance,
American Finance Association, vol. 46(2), pages 469-77, June.
- Theis Lange & Anders Rahbek & Søren Tolver Jensen, 2011. "Estimation and Asymptotic Inference in the AR-ARCH Model," Econometric Reviews, Taylor & Francis Journals, vol. 30(2), pages 129-153.
- Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
- 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.
- 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.
- Berkes, Istv n & Horv th, Lajos & Kokoszka, Piotr, 2003. "Estimation Of The Maximal Moment Exponent Of A Garch(1,1) Sequence," Econometric Theory, Cambridge University Press, vol. 19(04), pages 565-586, August.
- Slade, Margaret E, 1986. "Exogeneity Tests of Market Boundaries Applied to Petroleum Products," Journal of Industrial Economics, Wiley Blackwell, vol. 34(3), pages 291-303, March.
- Xavier Gabaix & Rustam Ibragimov, 2007.
"Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents,"
NBER Technical Working Papers
0342, National Bureau of Economic Research, Inc.
- Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
- MEITZ, Mika & SAIKKONEN, Pentti, 2006.
"Stability of nonlinear AR-GARCH models,"
CORE Discussion Papers
2006078, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Meitz, Mika & Saikkonen, Pentti, 2006. "Stability of nonlinear AR-GARCH models," SSE/EFI Working Paper Series in Economics and Finance 632, Stockholm School of Economics.
- Mika Meitz & Pentti Saikkonen, 2007. "Stability of nonlinear AR-GARCH models," Economics Series Working Papers 328, University of Oxford, Department of Economics.
- Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
- Hols, Martien C A B & de Vries, Casper G, 1991. "The Limiting Distribution of Extremal Exchange Rate Returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(3), pages 287-302, July-Sept.
- Wagner, Niklas & Marsh, Terry A., 2005. "Measuring tail thickness under GARCH and an application to extreme exchange rate changes," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 165-185, January.
- Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
- Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
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