Efficient Estimation in Semiparametric GARCH Models

F.C. Drost, C.A.J. Klaassen

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages29
Volume1996-38
Publication statusPublished - 1996

Publication series

NameCentER Discussion Paper
Volume1996-38

Fingerprint

GARCH Model
Efficient Estimation
Semiparametric Model
Adaptive Estimation
Autoregression
Generalized Autoregressive Conditional Heteroscedasticity
Nuisance Parameter
Conditional Heteroskedasticity
Autoregressive Conditional Heteroscedasticity
Reparametrization
Efficient Estimator
Score Function
Financial Data
Moment Conditions
Tangent Space
Integrated Model
Time Series Models
Parametric Model
Parametrization
Unknown Parameters

Keywords

  • garch models
  • estimation

Cite this

Drost, F. C., & Klaassen, C. A. J. (1996). Efficient Estimation in Semiparametric GARCH Models. (CentER Discussion Paper; Vol. 1996-38). Tilburg: Econometrics.
Drost, F.C. ; Klaassen, C.A.J. / Efficient Estimation in Semiparametric GARCH Models. Tilburg : Econometrics, 1996. (CentER Discussion Paper).
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Drost, FC & Klaassen, CAJ 1996 'Efficient Estimation in Semiparametric GARCH Models' CentER Discussion Paper, vol. 1996-38, Econometrics, Tilburg.

Efficient Estimation in Semiparametric GARCH Models. / Drost, F.C.; Klaassen, C.A.J.

Tilburg : Econometrics, 1996. (CentER Discussion Paper; Vol. 1996-38).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

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AU - Klaassen, C.A.J.

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N2 - 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.

AB - 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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Drost FC, Klaassen CAJ. Efficient Estimation in Semiparametric GARCH Models. Tilburg: Econometrics. 1996. (CentER Discussion Paper).