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Pseudo-Maximum Likelihood Estimation in Two Classes of Semiparametric Diffusion Models

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  • Dennis Kristensen

    () (Columbia University and CREATES)

Abstract

A novel estimation method for two classes of semiparametric scalar diffusion models is proposed: In the first class, the diffusion term is parameterised and the drift is left unspecified, while in the second class only the drift term is specified. Under the assumption of stationarity, the unspecified term can be identified as a functional of the parametric component and the stationary density. Given a discrete sample with a fixed time distance, the parametric component is then estimated by maximizing the associated likelihood with a preliminary estimator of the unspecified term plugged in. It is shown that this Pseudo-MLE (PMLE) is root n-consistent and asymptotically normally distributed under regularity conditions, and demonstrate how the models and estimators can be used in a two-step specification testing strategy of fully parametric models. Since the likelihood function is not available on closed form, the practical implementation of our estimator and tests will rely on simulated or approximate PMLE's. Under regularity conditions, it is verified that approximate/simulated versions of the PMLE inherits the properties of the actual but infeasible estimator. A simulation study investigates the finite-sample performance of the PMLE, and finds that it performs well and is comparable to parametric MLE both in terms of bias and variance.

Suggested Citation

  • Dennis Kristensen, 2009. "Pseudo-Maximum Likelihood Estimation in Two Classes of Semiparametric Diffusion Models," CREATES Research Papers 2009-41, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2009-41
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    Citations

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    Cited by:

    1. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    2. Shin Kanaya, 2015. "Uniform Convergence Rates of Kernel-Based Nonparametric Estimators for Continuous Time Diffusion Processes: A Damping Function Approach," CREATES Research Papers 2015-50, Department of Economics and Business Economics, Aarhus University.
    3. Kanaya, Shin & Kristensen, Dennis, 2016. "Estimation Of Stochastic Volatility Models By Nonparametric Filtering," Econometric Theory, Cambridge University Press, vol. 32(04), pages 861-916, August.
    4. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    5. repec:bok:journl:v:21:y:2015:i:4:p:28-58 is not listed on IDEAS
    6. Bu, Ruijun & Cheng, Jie & Hadri, Kaddour, 2016. "Reducible diffusions with time-varying transformations with application to short-term interest rates," Economic Modelling, Elsevier, vol. 52(PA), pages 266-277.
    7. Chen, Qiang & Zheng, Xu & Pan, Zhiyuan, 2015. "Asymptotically distribution-free tests for the volatility function of a diffusion," Journal of Econometrics, Elsevier, vol. 184(1), pages 124-144.
    8. Koo, Bonsoo & Linton, Oliver, 2012. "Estimation of semiparametric locally stationary diffusion models," Journal of Econometrics, Elsevier, vol. 170(1), pages 210-233.
    9. repec:eee:csdana:v:56:y:2012:i:12:p:3975-3987 is not listed on IDEAS
    10. 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.
    11. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Keywords

    Diffusion process; fixed-time distance asymptotics; kernel estimation; pseudo-likelihood; semiparametric;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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