Indirect estimation of GARCH models with alpha-stable innovations
Several studies have highlighted the fact that heavy-tailedness of asset returns can be the consequence of conditional heteroskedasticity. GARCH models have thus become very popular, given their ability to account for volatility clustering and, implicitly, heavy tails. However, these models encounter some difficulties in handling financial time series, as they respond equally to positive and negative shocks and their tail behavior remains too short even with Student-t error terms. To overcome these weaknesses we apply GARCH-type models with alpha-stable innovations. The stable family of distributions constitutes a generalization of the Gaussian distribution that has intriguing theoretical and practical properties. Indeed it is stable under addiction and, having four parameters, it allows for asymmetry and heavy tails. Unfortunately stable models do not have closed likelihood function, but since simulated values from α-stable distributions can be straightforwardly obtained, the indirect inference approach is particularly suited to the situation at hand. In this work we provide a description of how to estimate a GARCH(1,1) and a TGARCH(1,1) with symmetric stable shocks using as auxiliary model a GARCH(1,1) with skew-t innovations. Monte Carlo simulations, conducted using GAUSS, are presented and finally the proposed models are used to estimate the IBM weekly return series as an illustration of how they perform on real data.
|Date of creation:||18 Apr 2012|
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- Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-546, October.
- Roxana Chiriac & Valeri Voev, 2011.
"Modelling and forecasting multivariate realized volatility,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, 09.
- Roxana Chiriac & Valeri Voev, 2008. "Modelling and Forecasting Multivariate Realized Volatility," CREATES Research Papers 2008-39, Department of Economics and Business Economics, Aarhus University.
- Roxana Chiriac & Valeri Voev, 2008. "Modelling and Forecasting Multivariate Realized Volatility," CoFE Discussion Paper 08-06, .
- 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.
- Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
- Giorgio Calzolari & F. Di Iorio & G. Fiorentini, 1999. "Indirect Estimation of Just-Identified Models with Control Variates," Econometrics Working Papers Archive quaderno46, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
- Taleb, Nassim Nicholas, 2007. "Black Swans and the Domains of Statistics," The American Statistician, American Statistical Association, vol. 61, pages 198-200, August.
- 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.
- 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".
- Rafal Weron, 1996.
"Correction to: "On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables","
HSC Research Reports
HSC/96/01, Hugo Steinhaus Center, Wroclaw University of Technology.
- Weron, Rafal, 1996. "Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables"," MPRA Paper 20761, University Library of Munich, Germany, revised 2010.
- Gallant, A. Ronald & Tauchen, George, 1996.
"Which Moments to Match?,"
Cambridge University Press, vol. 12(04), pages 657-681, October.
- McCulloch, J. Huston, 1985. "Interest-risk sensitive deposit insurance premia : Stable ACH estimates," Journal of Banking & Finance, Elsevier, vol. 9(1), pages 137-156, March.
- Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
- Marco J. Lombardi & Giorgio Calzolari, 2004. "Indirect estimation of alpha-stable distributions and processes," Econometrics Working Papers Archive wp2004_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
- GARCIA, René & RENAULT, Eric & VEREDAS, David, 2006.
"Estimation of stable distributions by indirect inference,"
CORE Discussion Papers
2006112, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
- de Vries, Casper G., 1991.
"On the relation between GARCH and stable processes,"
Journal of Econometrics,
Elsevier, vol. 48(3), pages 313-324, June.
- de Vries, C.G., 1990. "On the relation between GARCH and stable processes," Discussion Paper 1990-34, Tilburg University, Center for Economic Research.
- 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.
- repec:cup:cbooks:9780521848053 is not listed on IDEAS
- 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.
- 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 273-285, July-Sept.
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