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Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models

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  • Kristensen, Dennis

Abstract

Two classes of semiparametric diffusion models are considered, where either the drift or the diffusion term is parameterized, while the other term is left unspecified. We propose a pseudo-maximum likelihood estimator (PMLE) of the parametric component that maximizes the likelihood with a preliminary estimator of the unspecified term plugged in. It is demonstrated how models and estimators can be used in a two-step specification testing strategy of semiparametric and fully parametric models, and shown that approximate/simulated versions of the PMLE inherit the properties of the actual but infeasible estimator. A simulation study investigates the finite sample performance of the PMLE.

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  • Kristensen, Dennis, 2010. "Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models," Journal of Econometrics, Elsevier, vol. 156(2), pages 239-259, June.
    • Handle: RePEc:eee:econom:v:156:y:2010:i:2:p:239-259
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    3. Zhang, Shulin & Song, Peter X.-K. & Shi, Daimin & Zhou, Qian M., 2012. "Information ratio test for model misspecification on parametric structures in stochastic diffusion models," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3975-3987.
    4. Kanaya, Shin, 2017. "Uniform Convergence Rates Of Kernel-Based Nonparametric Estimators For Continuous Time Diffusion Processes: A Damping Function Approach," Econometric Theory, Cambridge University Press, vol. 33(4), pages 874-914, August.
    5. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    6. 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.
    7. Koo, Bonsoo & Linton, Oliver, 2012. "Estimation of semiparametric locally stationary diffusion models," Journal of Econometrics, Elsevier, vol. 170(1), pages 210-233.
    8. Bu, Ruijun & Hadri, Kaddour & Kristensen, Dennis, 2021. "Diffusion copulas: Identification and estimation," Journal of Econometrics, Elsevier, vol. 221(2), pages 616-643.
    9. 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.
    10. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    11. Seungmoon Choi, 2015. "Maximum Likelihood Estimation of Continuous-Time Diffusion Models for Korean Short-Term Interest Rates," Economic Analysis (Quarterly), Economic Research Institute, Bank of Korea, vol. 21(4), pages 28-58, December.
    12. Buchholz, Nicholas & Shum, Matthew & Xu, Haiqing, 2021. "Semiparametric estimation of dynamic discrete choice models," Journal of Econometrics, Elsevier, vol. 223(2), pages 312-327.
    13. Ruijun Bu & Jihyun Kim & Bin Wang, 2020. "Uniform and Lp Convergences of Nonparametric Estimation for Diffusion Models," Working Papers 202021, University of Liverpool, Department of Economics.
    14. Bu, Ruijun & Kim, Jihyun & Wang, Bin, 2023. "Uniform and Lp convergences for nonparametric continuous time regressions with semiparametric applications," Journal of Econometrics, Elsevier, vol. 235(2), pages 1934-1954.
    15. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    Keywords

    Diffusion process Kernel estimation Pseudo-likelihood Semiparametric Testing;

    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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