Advanced Search
MyIDEAS: Login

Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model

Contents:

Author Info

  • Todd, Prono

Abstract

Efficient GMM estimation of the semi-strong GARCH(1,1) model requires simultaneous estimation of the conditional third and fourth moments. This paper proposes a simple alternative to efficient GMM based upon the unconditional skewness of residuals and the autocovariances of squared residuals. An advantage of this simple alternative is that neither the third nor the fourth conditional moment needs to be estimated. A second advantage is that linear estimators apply to all of the parameters in the model, making estimation straightforward in practice. The proposed estimators are IV-like with potentially many instruments. Sequential estimation involves TSLS in a first step followed by linear GMM. Simultaneous estimation involves either two-step GMM or CUE. A Monte Carlo study of the proposed estimators is included.

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/20034/
File Function: original version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/26190/
File Function: revised version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/27532/
File Function: revised version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/28540/
File Function: revised version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/33634/
File Function: revised version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 20034.

as in new window
Length:
Date of creation: Jan 2010
Date of revision:
Handle: RePEc:pra:mprapa:20034

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; Time Series Heteroskedasticity; GMM; CUE; Many Moments; Conditional Moment Restrictions; Consistency; Robust Statistics;

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. Rich, Robert W. & Raymond, Jennie & Butler, J. S., 1991. "Generalized instrumental variables estimation of autoregressive conditional heteroskedastic models," Economics Letters, Elsevier, vol. 35(2), pages 179-185, February.
  2. 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.
  3. Chirok Han & Peter C.B. Phillips, 2005. "GMM with Many Moment Conditions," Cowles Foundation Discussion Papers 1515, Cowles Foundation for Research in Economics, Yale University.
  4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  5. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  6. Taskinen, Sara & Oja, Hannu & Randles, Ronald H., 2005. "Multivariate Nonparametric Tests of Independence," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 916-925, September.
  7. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  8. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
  9. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
  10. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  11. Cragg, John G, 1983. "More Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form," Econometrica, Econometric Society, vol. 51(3), pages 751-63, May.
  12. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-19, March.
  13. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  14. MEDDAHI, Nour & RENAULT, Éric, 1998. "Quadratic M-Estimators for ARCH-Type Processes," Cahiers de recherche 9814, Universite de Montreal, Departement de sciences economiques.
  15. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  16. Escanciano, Juan Carlos, 2009. "Quasi-Maximum Likelihood Estimation Of Semi-Strong Garch Models," Econometric Theory, Cambridge University Press, vol. 25(02), pages 561-570, April.
  17. Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2009. "Merits and drawbacks of variance targeting in GARCH models," MPRA Paper 15143, University Library of Munich, Germany.
  18. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
  19. White, Halbert, 1982. "Instrumental Variables Regression with Independent Observations," Econometrica, Econometric Society, vol. 50(2), pages 483-99, March.
  20. Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences.
  21. Peter A. Zadrozny, 2005. "Necessary and Sufficient Restrictions for Existence of a Unique Fourth Moment of a Univariate GARCH(p,q) Process," CESifo Working Paper Series 1505, CESifo Group Munich.
  22. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
  23. Mark, Nelson C., 1988. "Time-varying betas and risk premia in the pricing of forward foreign exchange contracts," Journal of Financial Economics, Elsevier, vol. 22(2), pages 335-354, December.
  24. Skoglund, Jimmy, 2001. "A simple efficient GMM estimator of GARCH models," Working Paper Series in Economics and Finance 0434, Stockholm School of Economics.
  25. Asger Lunde & Peter Reinhard Hansen, 2001. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?," Working Papers 2001-04, Brown University, Department of Economics.
  26. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  27. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
  28. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
  29. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-80, July.
  30. Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 26-54.
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:20034. 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.