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Fully Nonparametric Estimation of Scalar Diffusion Models

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Author Info
Federico M. Bandi () (University of Chicago, IL, U.S.A)
Peter C. B. Phillips () (Yale University, New Haven, U.S.A.; University of Auckland, New Zealand; University of York, UK)

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Abstract

We propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process. We show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter. The asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens. We prove almost sure consistency and weak convergence to mixtures of normal laws, where the mixing variates depend on the chronological local time of the underlying diffusion process, that is the random time spent by the process in the vicinity of a generic spatial point. The estimation method and asymptotic results apply to both stationary and nonstationary recurrent processes. Copyright The Econometric Society 2003.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 71 (2003)
Issue (Month): 1 (January)
Pages: 241-283
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Handle: RePEc:ecm:emetrp:v:71:y:2003:i:1:p:241-283

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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. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. repec:cup:etheor:v:13:y:1997:i:5:p:615-45 is not listed on IDEAS
  3. Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
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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. 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!]
  2. Hao Zhou, 2001. "Jump-diffusion term structure and Ito conditional moment generator," Finance and Economics Discussion Series 2001-28, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  3. 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. Working paper #2," NCER Working Paper Series 2, National Centre for Econometric Research. [Downloadable!]
  4. Yacine Ait-Sahalia & Per A. Mykland, 2003. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," NBER Working Papers 9611, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  5. Hjalmarsson, Erik, 2003. "Does the Black-Scholes formula work for electricity markets? A nonparametric approach," Working Papers in Economics 101, Göteborg University, Department of Economics. [Downloadable!]
  6. 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:
  7. Arapis, Manuel & Gao, Jiti, 2004. "Empirical comparisons in short-term interest rate models using nonparametric methods," MPRA Paper 11974, University Library of Munich, Germany, revised 23 Dec 2005. [Downloadable!]
    Other versions:
  8. Park, Joon Y., 2005. "The Spatial Analysis of Time Series," Working Papers 2005-07, Rice University, Department of Economics. [Downloadable!]
  9. Fuchun Li, 2005. "Testing the Parametric Specification of the Diffusion Function in a Diffusion Process," Working Papers 05-35, Bank of Canada. [Downloadable!]
  10. Dennis Kristensen, 2007. "Nonparametric Estimation and Misspecification Testing of Diffusion Models," CREATES Research Papers 2007-01, School of Economics and Management, University of Aarhus. [Downloadable!]
  11. Hao Zhou, 2003. "Itô conditional moment generator and the estimation of short rate processes," Finance and Economics Discussion Series 2003-32, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
    Other versions:
  12. Javier Gil-Bazo & Gonzalo Rubio, 2003. "A Non-Parametric Dimension Test of the Term Structure," DFAEII Working Papers 200201, University of the Basque Country - Department of Foundations of Economic Analysis II. [Downloadable!]
  13. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
  14. Peter Spencer, 2004. "Affine Macroeconomic Models of the Term Structure of Interest Rates: The US Treasury Market 1961-99," Discussion Papers 04/16, Department of Economics, University of York, revised Jan 2006. [Downloadable!]
  15. Dennis Kristensen, 2008. "Uniform Convergence Rates of Kernel Estimators with Heterogenous, Dependent Data," CREATES Research Papers 2008-37, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  16. Qiying Wang & Peter C.B. Phillips, 2006. "Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1594, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  17. Peter C.B. Phillips & Jun Yu, 2005. "A Two-Stage Realized Volatility Approach to the Estimation for Diffusion Processes from Discrete Observations," Cowles Foundation Discussion Papers 1523, Cowles Foundation, Yale University. [Downloadable!]
  18. Roberto Reno', 2004. "Nonparametric Estimation of the Diffusion Coefficient via Fourier Analysis, with Aplication to Short Rate Modeling," Department of Economics University of Siena 440, Department of Economics, University of Siena. [Downloadable!]
  19. Roberto Reno' & Antonio Roma & Stephen Schaefer, 2004. "A Comparison of Alternative Nonparametric Estimators of the Short Rate Diffusion Coefficient," Department of Economics University of Siena 445, Department of Economics, University of Siena. [Downloadable!]
  20. Dennis Kristensen, 2007. "Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach," CREATES Research Papers 2007-02, School of Economics and Management, University of Aarhus. [Downloadable!]
  21. Peter C. B. Phillips & Jun Yu, 2005. "Comments on “A Selective Overview of Nonparametric Methods in Financial Econometrics” by Jianqing Fan," Working Papers 08-2005, Singapore Management University, School of Economics. [Downloadable!]
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