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Efficient estimation in semiparametric GARCH models

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Author Info
Drost, F.C.
Klaassen, C.A.J. (Tilburg University, Center for Economic Research)

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Abstract

It is well-known that financial data sets exhibit conditional heteroskedasticity. GARCH type models are often used to model this phenomenon. Since the distribution of the rescaled innovations is generally far from a normal distribution, a semiparametric approach is advisable. Several publications observed that adaptive estimation of the Euclidean parameters is not possible in the usual parametrization when the distribution of the rescaled innovations is the unknown nuisance parameter. However, there exists a reparametrization such that the efficient score functions in the parametric model of the autoregression parameters are orthogonal to the tangent space generated by the nuisance parameter, thus suggesting that adaptive estimation of the autoregression parameters is possible. Indeed, we construct adaptive and hence efficient estimators in a general GARCH in mean type context including integrated GARCH models.Our analysis is based on a general LAN Theorem for time-series models, published elsewhere. In contrast to recent literature about ARCH models we do not need any moment condition.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 38.

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Date of creation: 1996
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Handle: RePEc:dgr:kubcen:199638

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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.:
  1. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
    Other versions:
  2. Oliver Linton, 1993. "Adaptive Estimation in ARCH Models," Cowles Foundation Discussion Papers 1054, Cowles Foundation, Yale University. [Downloadable!]
  3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38. [Downloadable!] (restricted)
  4. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July. [Downloadable!] (restricted)
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  5. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March. [Downloadable!] (restricted)
  6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  7. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
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  8. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
  9. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199. [Downloadable!] (restricted)
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  10. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
  11. Steigerwald, Douglas G., 1992. "Adaptive estimation in time series regression models," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 251-275. [Downloadable!] (restricted)
  12. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun. [Downloadable!] (restricted)
  13. Robinson, P M, 1988. "Semiparametric Econometrics: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(1), pages 35-51, January. [Downloadable!] (restricted)
  14. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
  15. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  16. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
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(explanations, 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.)

  1. Andeaou, E. & Werker, B.J.M., 2004. "An alternative asymptotic analysis of residual-based statistics," Discussion Paper 56, Tilburg University, Center for Economic Research. [Downloadable!]
  2. Douglas Hodgson, 2002. "Semiparametric Efficient Estimation of the Mean of a Time Series in the Presence of Conditional Heterogeneity of Unknown Form," Cahiers de recherche CREFE / CREFE Working Papers 146, CREFE, Université du Québec à Montréal. [Downloadable!]
  3. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109. [Downloadable!]
  4. Peter Zadrozny, 2005. "Necessary and Sufficient Restrictions for Existence of a Unique Fourth Moment of a Univariate GARCH(p,q) Process," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH. [Downloadable!]
  5. Christian Francq & Jean-Michel Zakoïan, 2006. "Inference in GARCH when some coefficients are equal to zero," Computing in Economics and Finance 2006 64, Society for Computational Economics. [Downloadable!]
  6. Werker, B.J.M. & Andreou, E., 2003. "A simple asymptotic analysis of residual-based statistics," Discussion Paper 118, Tilburg University, Center for Economic Research. [Downloadable!]
  7. Drost, F.C. & Werker, B.J.M., 2001. "Semiparametric duration models," Discussion Paper 11, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  8. Takayuki Shiohama, 2006. "Asymptotically Efficient Estimation of the Change Point for Semiparametric GARCH models," Discussion Paper Series a471, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
  9. H. L"Utkepohl, . "Statistische Modellierung von Volatilit"aten," Sonderforschungsbereich 373 1996-70, Humboldt Universitaet Berlin.
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