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Semiparametric Efficient Estimation of the Mean of a Time Series in the Presence of Conditional Heterogeneity of Unknown Form

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Abstract

We obtain semiparametric efficiency bounds for the estimation of a location parameter in a time series model where the innovations are stationary and ergodic, conditionally symmetric martingale differences but otherwise possess general dependence and distributions of unknown form. We then describe an iterative estimator that achieves this bound when the conditional density functions of the sample are known. Finally, we develop a 'semi-adaptive' estimator that achieves the bound when these densities are unknown by the investigator. This estimator employs nonparametric kernel estimates of the densities. Monte Carlo results are reported. Nous dérivons une borne d'efficacité semi-paramétrique pour un estimateur de la moyenne d'une série temporelle dans un contexte où les innovations sont stationnaires et ergodiques. Nous supposons que les innovations suivent de façon conditionelle une différence de martingale symétrique tout en permettant une forme générale de dépendence temporelle et un loi de forme inconnue. Un estimateur «semi-adaptif» atteignant cette borne est proposé dans le cas où le fonction de densité est inconnue. Cet estimateur utilise une estimation non-paramétrique à noyau de la fonction de densité. Enfin, une étude de Monte-Carlo est présentée.

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Bibliographic Info

Paper provided by CREFE, Université du Québec à Montréal in its series Cahiers de recherche CREFE / CREFE Working Papers with number 146.

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Length: 35 pages
Date of creation: Jan 2002
Date of revision:
Handle: RePEc:cre:crefwp:146

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Keywords: Time series; semiparametric efficiency; conditional heteroskedasticity; adaptive estimation.;

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References

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  1. Oliver Linton, 1993. "Adaptive Estimation in ARCH Models," Cowles Foundation Discussion Papers 1054, Cowles Foundation for Research in Economics, Yale University.
  2. Kuersteiner, Guido M., 2002. "Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 18(03), pages 547-583, June.
  3. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
  4. Adrian R. Pagan & G. William Schwert, 1990. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
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  7. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1997. "Adaptive estimation in time-series models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74145, Tilburg University.
  8. Hodgson, Douglas J., 1998. "Adaptive Estimation Of Error Correction Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 44-69, February.
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  10. 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.
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  12. Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
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  14. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
  15. Steigerwald, Douglas G., 1992. "Adaptive estimation in time series regression models," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 251-275.
  16. Douglas Hodgson, 2000. "Unconditional pseudo-maximum likelihood and adaptive estimation in the presence of conditional heterogeneity of unknown form," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 175-206.
  17. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  18. Hodgson, Douglas J, 1999. "Adaptive Estimation of Cointegrated Models: Simulation Evidence and an Application to the Forward Exchange Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(6), pages 627-50, Nov.-Dec..
  19. repec:cup:etheor:v:11:y:1995:i:5:p:818-87 is not listed on IDEAS
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