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Semiparametric Estimation of Locally Stationary Diffusion Models

  • Bonsoo Koo
  • Oliver Linton

This paper proposes a class of locally stationary diffusion processes. The modelhas a time varying but locally linear drift and a volatility coefficient that is allowed tovary over time and space. We propose estimators of all the unknown quantitiesbased on long span data. Our estimation method makes use of the localstationarity. We establish asymptotic theory for the proposed estimators as thetime span increases. We apply this method to the real financial data to illustrate thevalidity of our model. Finally, we present a simulation study to provide the finitesampleperformance of the proposed estimators.

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File URL: http://sticerd.lse.ac.uk/dps/em/em551.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 /2010/551.

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Date of creation: Aug 2010
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Handle: RePEc:cep:stiecm:/2010/551
Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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  1. Bandi, Federico M. & Nguyen, Thong H., 2003. "On the functional estimation of jump-diffusion models," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 293-328.
  2. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, 02.
  3. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  4. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(05), pages 615-645, October.
  5. Stanton, Richard, 1997. " A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
  6. repec:bot:quadip:89 is not listed on IDEAS
  7. Federico M. Bandi & Peter C.B. Phillips, 2001. "Fully Nonparametric Estimation of Scalar Diffusion Models," Cowles Foundation Discussion Papers 1332, Cowles Foundation for Research in Economics, Yale University.
  8. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1433-1445, October.
  9. Piotr Fryzlewicz & Theofanis Sapatinas & Suhasini Subba Rao, 2008. "Normalized least-squares estimation in time-varying ARCH models," LSE Research Online Documents on Economics 25187, London School of Economics and Political Science, LSE Library.
  10. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
  11. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
  12. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
  13. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  14. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
  15. Phillips, P. C. B., 1973. "The problem of identification in finite parameter continuous time models," Journal of Econometrics, Elsevier, vol. 1(4), pages 351-362, December.
  16. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
  17. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
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