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Uniform and Lp Convergences of Nonparametric Estimation for Diffusion Models

Author

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  • Ruijun Bu
  • Jihyun Kim
  • Bin Wang

Abstract

We obtain the uniform convergence rates of nonparametric kernel estimators of the local time, the drift and volatility functions as well as their derivatives, of discretely sampled diffusion processes. Moreover, modified kernel estimators of the drift and volatility functions are considered and their Lp convergence rates are obtained. Our asymptotic results apply to recurrent diffusions which include both stationary or nonstationary cases. Our sampling scheme is two-dimensional, with sampling interval shrinking to zero and time span increasing to infinity jointly.

Suggested Citation

  • 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.
  • Handle: RePEc:liv:livedp:202021
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    File URL: https://www.liverpool.ac.uk/media/livacuk/schoolofmanagement/research/economics/Uniform,Lp,Convergences,Nonparametric,Estimation.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    recurrent; diffusion; kernel; uniform convergence; Lp convergence.;

    JEL classification:

    • 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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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