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Parameter Estimation for a Discretely Observed Integrated Diffusion Process

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  • ARNAUD GLOTER

Abstract

We consider the estimation of unknown parameters in the drift and diffusion coefficients of a one-dimensional ergodic diffusion ""X"" when the observation is a discrete sampling of the integral of ""X"" at times ""i"" Δ , ""i"" = 1 ,&h ellip;, ""n"" . Assuming that the sampling interval tends to 0 while the total length time interval tends to infinity, we first prove limit theorems for functionals associated with our observations. We apply these results to obtain a contrast function. The associated minimum contrast estimators are shown to be consistent and asymptotically Gaussian with different rates for drift and diffusion coefficient parameters. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

Suggested Citation

  • Arnaud Gloter, 2006. "Parameter Estimation for a Discretely Observed Integrated Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 83-104.
  • Handle: RePEc:bla:scjsta:v:33:y:2006:i:1:p:83-104
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    Citations

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    Cited by:

    1. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465.
    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. Samson, Adeline & Thieullen, Michèle, 2012. "A contrast estimator for completely or partially observed hypoelliptic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2521-2552.
    4. Benjamin Favetto, 2016. "Estimating functions for noisy observations of ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 19(1), pages 1-28, April.
    5. Arnaud Gloter, 2007. "Efficient estimation of drift parameters in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(4), pages 495-519, October.
    6. Comte, F. & Genon-Catalot, V. & Rozenholc, Y., 2009. "Nonparametric adaptive estimation for integrated diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 811-834, March.
    7. repec:eee:spapps:v:127:y:2017:i:11:p:3689-3718 is not listed on IDEAS
    8. 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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