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Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods

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Author Info
Oliver Linton
Enno Mammen

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Abstract

We investigate a class of semiparametric ARCH(8) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the 'news impact' function. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric and nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 daily returns. We find some evidence of asymmetric news impact functions in the data.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2003/453.

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Date of creation: May 2003
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Handle: RePEc:cep:stiecm:/2003/453

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Keywords: ARCH inverse problem kernel estimation news impact curve nonparametric regression profile likelihood semiparametric estimation volatility

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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. Carroll, Raymond J. & H rdle, Wolfgang & Mammen, Enno, 2002. "Estimation In An Additive Model When The Components Are Linked Parametrically," Econometric Theory, Cambridge University Press, vol. 18(04), pages 886-912, May. [Downloadable!]
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  2. Woocheol Kim & Oliver Linton, 2004. "A Local Instrumental Variable Estimation Method For Generalized Additive Volatility Models," FMG Discussion Papers dp509, Financial Markets Group. [Downloadable!] (restricted)
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  3. Darolles, S. & Florens, J.-P. & Renault, É., 2002. "Nonparametric Instrumental Regression," Cahiers de recherche 05-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
  4. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July. [Downloadable!] (restricted)
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  5. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290. [Downloadable!] (restricted)
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  6. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, March. [Downloadable!]
  7. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December. [Downloadable!] (restricted)
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  8. Joel Horowitz & Enno Mammen, 2002. "Nonparametric estimation of an additive model with a link function," CeMMAP working papers CWP19/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  9. DAROLLES, Serge & FLORENS, Jean-Pierre & RENAULT, Éric, 2002. "Nonparametric Instrumental Regression," Cahiers de recherche 2002-05, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  10. W. H"Ardle & A. Tsybakov & L. Yang, . "Nonparametric Vector Autoregression," Sonderforschungsbereich 373 1996-61, Humboldt Universitaet Berlin.
  11. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
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  12. Wu, Guojun & Xiao, Zhijie, 2002. "A generalized partially linear model of asymmetric volatility," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 287-319, August. [Downloadable!] (restricted)
  13. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199. [Downloadable!] (restricted)
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  14. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation, Yale University. [Downloadable!]
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  15. L. Yang & W. H"Ardle, . "Nonparametric Autoregression with Multiplicative Volatility and Additive Mean," Sonderforschungsbereich 373 1996-62, Humboldt Universitaet Berlin.
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  16. Oliver Linton, 1993. "Adaptive Estimation in ARCH Models," Cowles Foundation Discussion Papers 1054, Cowles Foundation, Yale University. [Downloadable!]
  17. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May. [Downloadable!] (restricted)
  18. repec:cup:etheor:v:13:y:1997:i:2:p:214-52 is not listed on IDEAS
  19. O. Linton & E. Mammen & J. Nielsen & C. Tanggaard, . "Estimating Yield Curves by Kernel Smoothing Methods," Sonderforschungsbereich 373 1999-54, Humboldt Universitaet Berlin.
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  20. Peter Hall & Joel L. Horowitz, 2003. "Nonparametric methods for inference in the presence of instrumental variables," CeMMAP working papers CWP02/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  21. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  22. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
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  23. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
  24. W. H"Ardle & O. Linton, . "Nonparametric Regression," Sonderforschungsbereich 373 1995-29, Humboldt Universitaet Berlin.
Full references

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. Oliver Linton & Enno Mammen, 2006. "Nonparametric Transformation to White Noise," STICERD - Econometrics Paper Series /2006/503, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  2. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society. [Downloadable!]
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