Indirect Estimation of α-Stable Garch Models
It is a well-known fact that financial returns exhibit conditional heteroscedasticity and fat tails. While the GARCH-type models are very popular in depicting the conditional heteroscedasticity, the α-stable distribution is a natural candidate for the conditional distribution of financial returns. The α-stable distribution is a generalization of the normal distribution and is described by four parameters, two of which deal with tail-thickness and asymmetry. However, practical implementation of α-stable distribution in finance applications has been limited by its estimation difficulties. In this paper, we propose an indirect approach of estimating GARCH models with α-stable innovations by using as auxiliary models GARCH-type models with Student's t distributed innovations. We provide comprehensive empirical evidence on the performance of the method within a series of Monte Carlo simulation studies and an empirical application to financial returns.
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- Seung‐Ryong Yang & B. Wade Brorsen, 1993. "Nonlinear dynamics of daily futures prices: Conditional heteroskedasticity or chaos?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 13(2), pages 175-191, 04.
- Ghose, Devajyoti & Kroner, Kenneth F., 1995. "The relationship between GARCH and symmetric stable processes: Finding the source of fat tails in financial data," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 225-251, September.
- Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
- Gourieroux, C. & Monfort, A. & Renault, E., 1992.
92.279, Toulouse - GREMAQ.
- Marco Lombardi & Giorgio Calzolari, 2006.
"Indirect estimation of alpha-stable stochastic volatility models,"
Econometrics Working Papers Archive
wp2006_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
- Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
- Tauchen, George E. & Gallant, A. Ronald, 1995.
"Which Moments to Match,"
95-20, Duke University, Department of Economics.
- Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-85, July-Sept.
- Marco J. Lombardi & Giorgio Calzolari, 2008. "Indirect Estimation of α-Stable Distributions and Processes," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 193-208, 03.
- de Vries, C.G., 1990.
"On the relation between GARCH and stable processes,"
1990-34, Tilburg University, Center for Economic Research.
- de Vries, Casper G., 1991. "On the relation between GARCH and stable processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 313-324, June.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Rene Garcia & Eric Renault & David Veredas, 2011. "Estimation of stable distributions with indirect inference," ULB Institutional Repository 2013/136186, ULB -- Universite Libre de Bruxelles.
- Liu, Shi-Miin & Brorsen, B Wade, 1995. "GARCH-Stable as a Model of Futures Price Movements," Review of Quantitative Finance and Accounting, Springer, vol. 5(2), pages 155-67, June.
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