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A Local Instrumental Variable Estimation Method For Generalized Additive Volatility Models

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  • Woocheol Kim
  • Oliver Linton

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Abstract

We investigate a new separable nonparametric model for time series, which includes many ARCH models and AR models already discussed in the literature. We also propose a new estimation procedure called LIVE, or local instrumental variable estimation, that is based on a localization of the classical instrumental variable method. Our method has considerable computational advantages over the competing marginal integration or projection method. We also consider a more efficient two-step likelihood-based procedure, and show that this yields both asymptotic and finite sample performance gains.

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File URL: http://www.lse.ac.uk/fmg/workingPapers/discussionPapers/fmgdps/dp509.pdf
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Bibliographic Info

Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp509.

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Date of creation: Sep 2004
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Handle: RePEc:fmg:fmgdps:dp509

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Web page: http://www.lse.ac.uk/fmg/

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  1. 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.
  2. repec:cup:etheor:v:13:y:1997:i:2:p:214-52 is not listed on IDEAS
  3. Oliver Linton & Jens Perch Nielsen & Sara van de Geer, 2001. "Estimating Multiplicative and Additive Hazard Functions by Kernel Methods," STICERD - Econometrics Paper Series /2001/411, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. 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.
  5. 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 for Research in Economics, Yale University.
  6. Wolfgang HÄRDLE & A. TSYBAKOV, 1995. "Local Polynomial Estimators of the Volatility Function in Nonparametric Autoregression," SFB 373 Discussion Papers 1995,42, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  7. Linton, Oliver B., 2000. "Efficient Estimation Of Generalized Additive Nonparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 16(04), pages 502-523, August.
  8. 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.
  9. Ziegelmann, Flavio A., 2002. "Nonparametric Estimation Of Volatility Functions: The Local Exponential Estimator," Econometric Theory, Cambridge University Press, vol. 18(04), pages 985-991, August.
  10. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  11. Donald W.K. Andrews, 1993. "Empirical Process Methods in Econometrics," Cowles Foundation Discussion Papers 1059, Cowles Foundation for Research in Economics, Yale University.
  12. Terasvirta, Timo & Tjostheim, Dag & W.J. Granger, Clive, 1986. "Aspects of modelling nonlinear time series," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 48, pages 2917-2957 Elsevier.
  13. Cai, Zongwu & Masry, Elias, 2000. "Nonparametric Estimation Of Additive Nonlinear Arx Time Series: Local Linear Fitting And Projections," Econometric Theory, Cambridge University Press, vol. 16(04), pages 465-501, August.
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Cited by:
  1. Oliver Linton & Enno Mammen, 2003. "Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods," STICERD - Econometrics Paper Series /2003/453, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.

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