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Simultaneously Modeling Conditional Heteroskedasticity And Scale Change

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Author Info
Feng, Yuanhua

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Abstract

This paper proposes a semiparametric approach by introducing a smooth scale function into the standard generalized autoregressive conditional heteroskedastic (GARCH) model so that conditional heteroskedasticity (CH) and scale change in financial returns can be modeled simultaneously. An estimation procedure combining kernel estimation of the scale function and maximum likelihood estimation of the GARCH parameters is proposed. Asymptotic properties of the estimators are investigated in detail. It is shown that asymptotically normal, -consistent parameter estimation is available. A data-driven algorithm is developed for practical implementation. Finite sample performance of the proposal is studied through simulation. The proposal is applied to model CH and scale change in the daily S P 500 and DAX 100 returns. It is shown that both series have simultaneously significant scale change and CH.We are very grateful to the co-editor and two referees for their helpful comments and suggestions, which led to a substantial improvement of this paper. The paper was finished under the advice of Professor Jan Beran, Department of Mathematics and Statistics, University of Konstanz, Germany, and was financially supported by the Center of Finance and Econometrics (CoFE), University of Konstanz. We thank colleagues in CoFE, especially Professor Winfried Pohlmeier, for their interesting questions at a talk of the author. It was these questions that motivated the author to write this paper. Our special thanks go to Dr. Erik L ders, Department of Finance and Insurance, Laval University, and Stern School of Business, New York University, for his helpful suggestions.

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

Volume (Year): 20 (2004)
Issue (Month): 03 (June)
Pages: 563-596
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Handle: RePEc:cup:etheor:v:20:y:2004:i:03:p:563-596_20

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References listed on IDEAS
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.:
  1. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June. [Downloadable!]
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  2. Beran, Jan & Feng, Yuanhua, 2002. "SEMIFAR models--a semiparametric approach to modelling trends, long-range dependence and nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 393-419, August. [Downloadable!] (restricted)
  3. W. H"Ardle & A. Tsybakov & L. Yang, . "Nonparametric Vector Autoregression," Sonderforschungsbereich 373 1996-61, Humboldt Universitaet Berlin.
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  5. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May. [Downloadable!] (restricted)
  6. Jan Beran & Yuanhua.Feng, 2001. "Iterative plug-in algorithms for SEMIFAR models - definition, convergence and asymptotic properties," CoFE Discussion Paper 01-11, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  7. Jan Beran & Yuanhua Feng, 1999. "Local Polynomial Estimation with a FARIMA-GARCH Error Process," CoFE Discussion Paper 99-08, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  8. Jan Beran & Yuanhua Feng, 2002. "Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(2), pages 291-311, June. [Downloadable!] (restricted)
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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.)

  1. Yuanhua Feng, 2002. "Modelling Different Volatility Components in High-Frequency Financial Returns," CoFE Discussion Paper 02-18, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  2. Feng, Yuanhua & Yu, Keming, 2006. "Nonparametric estimation of time-varying covariance matrix in a slowly changing vector random walk model," MPRA Paper 1597, University Library of Munich, Germany. [Downloadable!]
  3. Jan Beran & Yuanhua.Feng, 2002. "Recent Developments in Non- and Semiparametric Regression with Fractional Time Series Errors," CoFE Discussion Paper 02-13, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  4. Feng, Yuanhua, 2006. "A local dynamic conditional correlation model," MPRA Paper 1592, University Library of Munich, Germany. [Downloadable!]
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