# Empirical likelihood-based inference for nonparametric recurrent diffusions

## Author Info

• Xu, Ke-Li
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## 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.

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## Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 153 (2009)
Issue (Month): 1 (November)
Pages: 65-82

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Handle: RePEc:eee:econom:v:153:y:2009:i:1:p:65-82

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Web page: http://www.elsevier.com/locate/jeconom

## Related research

Keywords: Confidence interval Continuous-time models Diffusion Drift Empirical likelihood Local linear smoothing Local time Nonparametric estimation Nonstationarity Stochastic differential equation;

## References

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## Citations

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Cited by:
1. 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.
2. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(02), pages 541-563, April.
3. 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.

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