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Estimating Semiparametric ARCH Models by Kernel Smoothing Methods

  • Enno Mammen
  • Oliver Linton

    ()

We investigate a class of semiparametric ARCH 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 show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. 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 index returns. We find evidence of asymmetric news impact functions, consistent with the parametric analysis.

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Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp511.

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Date of creation: Sep 2004
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Handle: RePEc:fmg:fmgdps:dp511
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  1. Adrian R. Pagan & G. William Schwert, 1989. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
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  3. Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
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  8. Oliver Linton, 1993. "Adaptive Estimation in ARCH Models," Cowles Foundation Discussion Papers 1054, Cowles Foundation for Research in Economics, Yale University.
  9. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(02), pages 214-252, April.
  10. 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.
  11. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  12. 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, August.
  13. 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.
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  19. repec:att:wimass:9429 is not listed on IDEAS
  20. Oliver Linton & Enno Mammen & Jens Perch Nielsen & C Tanggaard, 2000. "Yield Curve Estimation by Kernel Smoothing Methods," STICERD - Econometrics Paper Series 385, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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  25. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  26. Horowitz, Joel L. & Mammen, Enno, 2002. "Nonparametric estimation of an additive model with a link function," SFB 373 Discussion Papers 2002,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  27. Yang, Lijian & Härdle, Wolfgang & Nielsen, Jens P., 1998. "Nonparametric autoregression with multiplicative volatility and additive mean," SFB 373 Discussion Papers 1998,107, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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