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Indirect Estimation of α-Stable Garch Models

Author

Listed:
  • Giorgio Calzolari

    () (Dipartimento di Statistica "G. Parenti", Università di Firenze, Italy)

  • Roxana Halbleib

    () (Department of Economics, University of Konstanz, Germany)

  • Alessandro Parrini

    () (Vrije Universiteit Amsterdam, The Netherlands)

Abstract

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.

Suggested Citation

  • Giorgio Calzolari & Roxana Halbleib & Alessandro Parrini, 2012. "Indirect Estimation of α-Stable Garch Models," Working Paper Series of the Department of Economics, University of Konstanz 2012-31, Department of Economics, University of Konstanz.
    • Handle: RePEc:knz:dpteco:1231
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    References listed on IDEAS

    as
    1. 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.
    2. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    3. 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.
    4. Rene Garcia & Eric Renault & David Veredas, 2011. "Estimation of stable distributions with indirect inference," ULB Institutional Repository 2013/136186, ULB -- Universite Libre de Bruxelles.
    5. 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, April.
    6. de Vries, Casper G., 1991. "On the relation between GARCH and stable processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 313-324, June.
    7. 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.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    10. 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.
    11. 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, March.
    12. 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 155-167, June.
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    More about this item

    Keywords

    Indirect Inference; α-stable Distribution; GARCH Models; Student's t Distribution;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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