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Nonparametric Estimation Of Second-Order Stochastic Differential Equations

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  • Nicolau, João

Abstract

We propose nonparametric estimators of the infinitesimal coefficients associated with second-order stochastic differential equations. We show that under appropriate conditions, the proposed estimators are consistent. Also, we state conditions ensuring the asymptotic normality of these estimators. We conclude our paper with a Monte Carlo experiment in which we assess the response of the nonparametric estimators with respect to the step of discretization.I thank two anonymous referees who made valuable suggestions that led to considerable improvements in the paper. I am also grateful to Carlos Braumann and Tom Kundert for helpful comments. This research was supported by the Fundação para a Ciência e a Tecnologia (FCT) and by FEDER/POCI 2010.

Suggested Citation

  • Nicolau, João, 2007. "Nonparametric Estimation Of Second-Order Stochastic Differential Equations," Econometric Theory, Cambridge University Press, vol. 23(5), pages 880-898, October.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:05:p:880-898_07
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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. Nicolau, João, 2008. "Modeling financial time series through second-order stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2700-2704, November.
    3. Tianshun Yan & Changlin Mei, 2017. "A test for a parametric form of the volatility in second-order diffusion models," Computational Statistics, Springer, vol. 32(4), pages 1583-1596, December.
    4. Yunyan Wang & Lixin Zhang & Mingtian Tang, 2012. "Re-weighted functional estimation of second-order diffusion processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1129-1151, November.

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