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A Two-Stage Realized Volatility Approach to the Estimation for Diffusion Processes from Discrete Observations

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)
Jun Yu

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Abstract

This paper motivates and introduces a two-stage method for estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as recently developed in Barndorff-Nielsen and Shephard (2002), to provide a regression model for estimating the parameters in the diffusion function. In the second stage the in-fill likelihood function is derived by means of the Girsanov theorem and then used to estimate the parameters in the drift function. Consistency and asymptotic distribution theory for these estimates are established in various contexts. The finite sample performance of the proposed method is compared with that of the approximate maximum likelihood method of Ait-Sahalia (2002).

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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1523.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1523.

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Length: 27 pages
Date of creation: Jun 2005
Date of revision:
Handle: RePEc:cwl:cwldpp:1523

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Maximum likelihood; Girsnov theorem; Discrete sampling; Continuous record; Realized volatility;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Jun Yu & Peter Phillips, 2004. "Jackknifing Bond Option Prices," Econometric Society 2004 North American Winter Meetings 115, Econometric Society. [Downloadable!]
    Other versions:
  2. Federico M. Bandi & Peter C.B. Phillips, 2005. "A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions," Cowles Foundation Discussion Papers 1522, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, 08. [Downloadable!] (restricted)
  4. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  5. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July. [Downloadable!] (restricted)
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  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  7. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January. [Downloadable!] (restricted)
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  8. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280. [Downloadable!] (restricted)
    Other versions:
  9. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-93, July.
    Other versions:
  10. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 12(4), pages 721-62.
  11. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers 2001-W16, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  12. Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-91, April.
  13. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  2. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Seeing the wood for the trees: A critical evaluation of methods to estimate the parameters of stochastic differential equations," Stan Hurn Discussion Papers 2006, School of Economics and Finance, Queensland University of Technology. [Downloadable!]
  3. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," Economics Papers 2005-W16, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
    Other versions:
  4. Arnaud Gloter, 2007. "Efficient estimation of drift parameters in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(4), pages 495-519, October. [Downloadable!] (restricted)
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