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Efficient estimation in semiparametric GARCH models

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Author Info

  • Drost, Feike C.
  • Klaassen, Chris A. J.

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 81 (1997)
Issue (Month): 1 (November)
Pages: 193-221

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Handle: RePEc:eee:econom:v:81:y:1997:i:1:p:193-221

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. 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.
  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. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
  4. 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.
  5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  6. Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
  7. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  8. Steigerwald, Douglas G., 1995. "Reply to B.M. Potscher's comment on 'adaptive estimation in time series regression models'," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 131-132.
  9. Robinson, P M, 1988. "Semiparametric Econometrics: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(1), pages 35-51, January.
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  11. 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.
  12. Kreiss Jens-Peter, 1987. "On Adaptive Estimation In Autoregressive Models When There Are Nuisance Functions," Statistics & Risk Modeling, De Gruyter, vol. 5(1-2), pages 59-76, February.
  13. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  14. 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.
  15. Steigerwald, Douglas G., 1992. "Adaptive estimation in time series regression models," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 251-275.
  16. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
  17. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  18. 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.
  19. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August.
  20. 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.
  21. Gourieroux Christian & Monfort Alain, 1991. "Qualitative threshold arch models," CEPREMAP Working Papers (Couverture Orange) 9109, CEPREMAP.
  22. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
  23. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
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