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Empirical likelihood-based inference for nonparametric recurrent diffusions

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  • Xu, Ke-Li

Abstract

This paper provides a new approach to constructing confidence intervals for nonparametric drift and diffusion functions in the continuous-time diffusion model via empirical likelihood (EL). The log EL ratios are constructed through the estimating equations satisfied by the local linear estimators. Limit theories are developed by means of increasing time span and shrinking observational intervals. The results apply to both stationary and nonstationary recurrent diffusion processes. Simulations show that for both drift and diffusion functions, the new procedure performs remarkably well in finite samples and clearly dominates the conventional method in constructing confidence intervals based on asymptotic normality. An empirical example is provided to illustrate the usefulness of the proposed method.

Suggested Citation

  • Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
  • Handle: RePEc:eee:econom:v:153:y:2009:i:1:p:65-82
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(02), pages 541-563, April.
    2. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    3. 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.
    4. Song, Yuping & Lin, Zhengyan, 2013. "Empirical likelihood inference for the second-order jump-diffusion model," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 184-195.
    5. repec:spr:annopr:v:256:y:2017:i:2:d:10.1007_s10479-016-2273-6 is not listed on IDEAS
    6. Márcio Poletti Laurini & Luiz Koodi Hotta, 2016. "Generalized moment estimation of stochastic differential equations," Computational Statistics, Springer, vol. 31(3), pages 1169-1202, September.
    7. Yunyan Wang & Lixin Zhang, 2013. "Local linear estimation for stochastic processes driven by $$\alpha $$ α -stable L $$\acute{\mathbf{e}}$$ e ´ vy motion," Statistical Inference for Stochastic Processes, Springer, vol. 16(2), pages 161-171, July.
    8. YABE, Ryota, 2014. "Empirical Likelihood Confidence Intervals for Nonparametric Nonlinear Nonstationary Regression Models," Discussion Papers 2014-20, Graduate School of Economics, Hitotsubashi University.

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