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Efficient estimation in semiparametric GARCH models

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  • Drost, F.C.

    (Tilburg University)

  • Klaassen, C.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

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-74146.

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Date of creation: 1997
Date of revision:
Publication status: Published in Journal of Econometrics (1997) v.81, p.193-221
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-74146

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Web page: http://www.tilburguniversity.edu/

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  1. Werker, B.J.M. & Drost, F.C., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-72561, Tilburg University.
  2. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
  3. Robinson, P M, 1988. "Semiparametric Econometrics: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 3(1), pages 35-51, January.
  4. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 159-199.
  5. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 7(3), pages 297-305, July.
  6. Steigerwald, Douglas G., 1995. "Reply to B.M. Potscher's comment on 'adaptive estimation in time series regression models'," Journal of Econometrics, Elsevier, Elsevier, vol. 66(1-2), pages 131-132.
  7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  8. Kreiss Jens-Peter, 1987. "On Adaptive Estimation In Autoregressive Models When There Are Nuisance Functions," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 5(1-2), pages 59-76, February.
  9. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  10. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper, Tilburg University, Center for Economic Research 1994-88, Tilburg University, Center for Economic Research.
  11. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
  12. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(05), pages 818-887, October.
  13. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-153273, Tilburg University.
  14. Oliver Linton, 1993. "Adaptive Estimation in ARCH Models," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1054, Cowles Foundation for Research in Economics, Yale University.
  15. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  16. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 9(4), pages 345-59, October.
  17. 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, Econometric Society, vol. 55(2), pages 391-407, March.
  18. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 2(01), pages 107-131, April.
  19. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
  20. Steigerwald, Douglas G., 1992. "Adaptive estimation in time series regression models," Journal of Econometrics, Elsevier, Elsevier, vol. 54(1-3), pages 251-275.
  21. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 10(01), pages 29-52, March.
  22. 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.
  23. 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, Elsevier, vol. 52(1-2), pages 5-59.
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