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A Local Instrumental Variable Estimation Method for Generalized Additive Volatility Models

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  • Woocheol Kim
  • Oliver Linton

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 based on a localization of the econometric method of instrumental variables. Our method has considerable computational advantages over the competing marginal integration or projection method.

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File URL: http://sticerd.lse.ac.uk/dps/em/em456.pdf
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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 /2003/456.

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Date of creation: May 2003
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Handle: RePEc:cep:stiecm:/2003/456

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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Keywords: ARCH; kernel estimation; nonparametric; volatility.;

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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. 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.
  3. 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.
  4. 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.
  5. repec:cup:etheor:v:13:y:1997:i:2:p:214-52 is not listed on IDEAS
  6. O. B. LINTON & R. CHEN & Wolfgang HÄRDLE, 1995. "An Analysis of Transformations for Additive Nonparanetric Regression," SFB 373 Discussion Papers 1995,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  7. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
  8. 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.
  9. Andrews, Donald W.K., 1986. "Empirical process methods in econometrics," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 37, pages 2247-2294 Elsevier.
  10. L. YANG & Wolfgang HÄRDLE, 1996. "Nonparametric Autoregression with Multiplicative Volatility and Additive Mean," SFB 373 Discussion Papers 1996,62, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  11. Oliver Linton, 2000. "Efficient estimation of generalized additive nonparametric regression models," LSE Research Online Documents on Economics 314, London School of Economics and Political Science, LSE Library.
  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. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  14. Wolfgang HÄRDLE & A. TSYBAKOV & L. YANG, 1996. "Nonparametric Vector Autoregression," SFB 373 Discussion Papers 1996,61, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  15. 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.
  16. 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.
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Cited by:
  1. 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.
  2. Oliver Linton & Enno Mammen, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.

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