Advanced Search
MyIDEAS: Login to save this paper or follow this series

Indirect estimation of GARCH models with alpha-stable innovations

Contents:

Author Info

  • Parrini, Alessandro

Abstract

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://mpra.ub.uni-muenchen.de/38544/
File Function: original version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 38544.

as in new window
Length:
Date of creation: 18 Apr 2012
Date of revision:
Handle: RePEc:pra:mprapa:38544

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC

Related research

Keywords: GARCH; alpha-stable distribution; indirect estimation; skew-t distribution; Monte Carlo simulations;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 53(6), pages 2298-2308, April.
  2. 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.
  3. Roxana Chiriac & Valeri Voev, 2008. "Modelling and Forecasting Multivariate Realized Volatility," CREATES Research Papers 2008-39, School of Economics and Management, University of Aarhus.
  4. 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, American Statistical Association, vol. 21(4), pages 532-46, October.
  5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  6. 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.
  7. GARCIA, René & RENAULT, Eric & VEREDAS, David, 2006. "Estimation of stable distributions by indirect inference," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2006112, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 12(04), pages 657-681, October.
  9. McCulloch, J. Huston, 1985. "Interest-risk sensitive deposit insurance premia : Stable ACH estimates," Journal of Banking & Finance, Elsevier, Elsevier, vol. 9(1), pages 137-156, March.
  10. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 6(03), pages 318-334, September.
  11. Marco J. Lombardi & Giorgio Calzolari, 2004. "Indirect estimation of alpha-stable distributions and processes," Econometrics Working Papers Archive, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" wp2004_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  12. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, Elsevier, vol. 28(2), pages 165-171, June.
  13. Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 10(3), pages 273-85, July-Sept.
  14. de Vries, Casper G., 1991. "On the relation between GARCH and stable processes," Journal of Econometrics, Elsevier, Elsevier, vol. 48(3), pages 313-324, June.
  15. Giorgio Calzolari & F. Di Iorio & G. Fiorentini, 1999. "Indirect Estimation of Just-Identified Models with Control Variates," Econometrics Working Papers Archive, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" quaderno46, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  16. Taleb, Nassim Nicholas, 2007. "Black Swans and the Domains of Statistics," The American Statistician, American Statistical Association, American Statistical Association, vol. 61, pages 198-200, August.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:38544. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.