Adaptive Estimation in ARCH Models

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Adaptive Estimation in ARCH Models

Author Info

Linton, Oliver

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Oliver Bruce Linton

Abstract

We construct efficient estimators of the identifiable parameters in a regression model when the errors follow a stationary parametric ARCH(P) process. We do not assume a functional form for the conditional density of the errors, but do require that it be symmetric about zero. The estimators of the mean parameters are adaptive in the sense of Bickel [2]. The ARCH parameters are not jointly identifiable with the error density. We consider a reparameterization of the variance process and show that the identifiable parameters of this process are adaptively estimable.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 9 (1993)
Issue (Month): 04 (August)
Pages: 539-569
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Handle: RePEc:cup:etheor:v:9:y:1993:i:04:p:539-569_00

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Paper
- Oliver Linton, 1993. "Adaptive Estimation in ARCH Models," Cowles Foundation Discussion Papers 1054, Cowles Foundation, Yale University. [Downloadable!]

Cited by:
(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.)

Douglas J. Hodgson & Oliver Linton & Keith Vorkink, 2001. "Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach," Cahiers de recherche CREFE / CREFE Working Papers 143, CREFE, Université du Québec à Montréal. [Downloadable!]
Other versions:
- Oliver Linton & Douglas J.Hodgson & Keith Vorkink, 2001. "Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach," FMG Discussion Papers dp382, Financial Markets Group. [Downloadable!] (restricted)
- Douglas J Hodgson & Oliver Linton & Keith Vorkink, 2000. "Testing the Capital Asset Pricing Model Efficiently under Elliptical Symmetry: A Semiparametric Approach," STICERD - Econometrics Paper Series /2000/398, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
- Keith Vorkink & Douglas J. Hodgson & Oliver Linton, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639. [Downloadable!]
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!]
Nour Meddahi & Éric Renault, 1998. "Quadratic M-Estimators for ARCH-Type Processes," CIRANO Working Papers 98s-29, CIRANO. [Downloadable!]
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!]
Thanasis Stengos & Ximing Wu, 2005. "Partially Adaptive Estimation via Maximum Entropy Densities," University of Cyprus Working Papers in Economics 6-2005, University of Cyprus Department of Economics. [Downloadable!]
Thanasis Stengos & Yiguo Sun, 2005. "The Absolute Health Income Hypothesis Revisited : A Semiparametric Quantile Regression Approach," University of Cyprus Working Papers in Economics 7-2005, University of Cyprus Department of Economics. [Downloadable!]
Other versions:
- Thanasis Stengos & Yiguo Sun, 2007. "The absolute health income hypothesis revisited: A Semiparametric Quantile Regression Approach," Working Paper Series 23-07, Rimini Centre for Economic Analysis, revised Jul 2007. [Downloadable!]
- Thanasis Stengos & Yiguo Sun, 2006. "The absolute health income hypothesis revisited: A Semiparametric Quantile Regression Approach," Working Papers 0606, University of Guelph, Department of Economics. [Downloadable!]
- Yiguo Sun & Thanasis Stengos, 2008. "The absolute health income hypothesis revisited: a semiparametric quantile regression approach," Empirical Economics, Springer, vol. 35(2), pages 395-412, September. [Downloadable!] (restricted)
Douglas J. Hodgson & Keith Vorkink, 2001. "Efficient Estimation of Conditional Asset Pricing Models," Cahiers de recherche CREFE / CREFE Working Papers 144, CREFE, Université du Québec à Montréal. [Downloadable!]
Other versions:
- Hodgson, Douglas J & Vorkink, Keith P, 2003. "Efficient Estimation of Conditional Asset-Pricing Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 269-83, April.
Oliver Linton, 1994. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Cowles Foundation Discussion Papers 1086, Cowles Foundation, Yale University. [Downloadable!]
Other versions:
- Linton, Oliver, 1996. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 12(01), pages 30-60, March. [Downloadable!]
Emma M. Iglesias & Oliver Linton, 2009. "Estimation of tail thickness parameters from GJR-GARCH models," Economics Working Papers we094726, Universidad Carlos III, Departamento de Economía. [Downloadable!]
Oliver Linton & Enno Mammen, 2003. "Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods," STICERD - Econometrics Paper Series /2003/453, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
Other versions:
- Enno Mammen & Oliver Linton, 2004. "Estimating Semiparametric ARCH Models by Kernel Smoothing Methods," FMG Discussion Papers dp511, Financial Markets Group. [Downloadable!] (restricted)
HAFNER, Christian & ROMBOUTS, Jeroen, 2003. "Semiparametric multivariate GARCH models," CORE Discussion Papers 2003003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
Douglas Hodgson & Barrett Slade & Keith Vorkink, 2006. "Constructing Commercial Indices: A Semiparametric Adaptive Estimator Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 32(2), pages 151-168, March. [Downloadable!] (restricted)
Drost, F.C. & Werker, B.J.M., 2001. "Semiparametric duration models," Discussion Paper 11, Tilburg University, Center for Economic Research. [Downloadable!]
Other versions:
- Drost, Feike C & Werker, Bas J M, 2004. "Semiparametric Duration Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 40-50, January.
Enrique Sentana & Gabriele Fiorentini, 2007. "On The Efficiency And Consistency Of Likelihood Estimation In Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI. [Downloadable!]
Other versions:
- Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper Series 38-07, Rimini Centre for Economic Analysis, revised Jul 2007. [Downloadable!]
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!]
Oliver Linton & Douglas G. Steigerwald, 1995. "Adaptive Testing in ARCH Models," Cowles Foundation Discussion Papers 1105, Cowles Foundation, Yale University. [Downloadable!]
Other versions:
- Oliver Linton & Douglas Steigerwald, 2000. "Adaptive testing in arch models," Econometric Reviews, Taylor and Francis Journals, vol. 19(2), pages 145-174. [Downloadable!] (restricted)
Drost, F.C. & Klaassen, C.A.J., 1996. "Efficient estimation in semiparametric GARCH models," Discussion Paper 38, Tilburg University, Center for Economic Research. [Downloadable!]
Other versions:
- Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November. [Downloadable!] (restricted)

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This page was last updated on 2009-11-24.

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