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Estimating Semiparametric ARCH Models by Kernel Smoothing Methods

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  • Enno Mammen
  • Oliver Linton

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Abstract

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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Bibliographic Info

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. Woocheol Kim & Oliver Linton, 2004. "A Local Instrumental Variable Estimation Method For Generalized Additive Volatility Models," FMG Discussion Papers dp509, Financial Markets Group.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Oliver Linton & Enno Mammen & N Nielsen, 2000. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions," STICERD - Econometrics Paper Series /2000/386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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  6. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  7. 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.
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  10. 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.
  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.
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  17. 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.
  18. John Rust & Department of Economics & University of Wisconsin, 1994. "Using Randomization to Break the Curse of Dimensionality," Computational Economics 9403001, EconWPA, revised 04 Jul 1994.
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  20. Drost, F.C. & Klaassen, C.A.J., 1996. "Efficient Estimation in Semiparametric GARCH Models," Discussion Paper 1996-38, Tilburg University, Center for Economic Research.
  21. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August.
  22. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(02), pages 258-289, February.
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  24. 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.
  25. 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, February.
  26. 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.
  27. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
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Citations

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Cited by:
  1. Christian M. Dahl & Emma M. Iglesias, 2008. "The limiting properties of the QMLE in a general class of asymmetric volatility models," CREATES Research Papers 2008-38, School of Economics and Management, University of Aarhus.
  2. Gregory Connor & Matthias Hagmann & Oliver Linton, 2007. "Efficient Estimation of a SemiparametricCharacteristic-Based Factor Model of Security Returns," STICERD - Econometrics Paper Series /2007/524, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. 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.
  4. Jean-Marie Dufour & René García & Abderrahim Taamouti, 2008. "Measuring causality between volatility and returns with high-frequency data," Economics Working Papers we084422, Universidad Carlos III, Departamento de Economía.
  5. Li, Degui & Lu, Zudi & Linton, Oliver, 2012. "Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates," Econometric Theory, Cambridge University Press, vol. 28(05), pages 935-958, October.
  6. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society.
  7. Christian Conrad & Enno Mammen, 2008. "Nonparametric Regression on Latent Covariates with an Application to Semiparametric GARCH-in-Mean Models," Working Papers 0473, University of Heidelberg, Department of Economics, revised Jul 2008.
  8. Linton, Oliver B. & Mammen, Enno, 2008. "Nonparametric transformation to white noise," Journal of Econometrics, Elsevier, vol. 142(1), pages 241-264, January.

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