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Simultaneously Modelling Conditional Heteroskedasticity and Scale Change

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Author Info
Yuanhua Feng () (Department of Mathematics and Statistics, University of Konstanz)

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Abstract

This paper proposes a semiparametric approach by introducing a smooth scale function into the standard GARCH model so that conditional heteroskedasticity and scale change in a financial time series can be modelled simultaneously. An estimation procedure combining kernel estimation of the scale function and maximum likelihood estimation of the GARCH parameters is proposed. Asymptotic proper- ties of the kernel estimator are investigated in detail. An iterative plug-in algorithm is developed for selecting the bandwidth. Practical performance of the proposal is illustrated by simulation. The proposal is applied to the daily S&P 500 and DAX 100 returns. It is shown that there are simultaneously significant conditional heteroskedasticity and scale change in these series.

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Publisher Info
Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 02-12.

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Length: 32 pages
Date of creation: Apr 2002
Date of revision:
Handle: RePEc:knz:cofedp:0212

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Related research
Keywords: Semiparametric GARCH; conditional heteroskedasticity; scale change; nonparametric regression with dependence; bandwidth selection;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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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. 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)
  2. 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!]
  3. 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!]
    Other versions:
  4. W. H"Ardle & A. Tsybakov & L. Yang, . "Nonparametric Vector Autoregression," Sonderforschungsbereich 373 1996-61, Humboldt Universitaet Berlin.
  5. 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)
  6. 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)
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  8. 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!]
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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. Feng, Yuanhua, 2006. "A local dynamic conditional correlation model," MPRA Paper 1592, University Library of Munich, Germany. [Downloadable!]
  2. 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!]
  3. 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!]
  4. 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!]
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