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Wavelet estimation in diffusions with periodicity

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  • Michael Diether

Abstract

We consider a time-inhomogeneous diffusion process, whose drift term contains a deterministic T-periodic signal with known periodicity. This signal is supposed to be contained in a Besov space, we try to estimate it using a non-parametric wavelet estimator. Our estimator is inspired by the thresholded wavelet density estimator constructed by Donoho, Johnstone, Kerkyacharian and Picard in 1996. Under certain ergodicity assumptions to the process, we can give the same asymptotic rate of convergence as for the density estimator. Copyright Springer Science+Business Media Dordrecht 2012

Suggested Citation

  • Michael Diether, 2012. "Wavelet estimation in diffusions with periodicity," Statistical Inference for Stochastic Processes, Springer, vol. 15(3), pages 257-284, October.
    • Handle: RePEc:spr:sistpr:v:15:y:2012:i:3:p:257-284
    DOI: 10.1007/s11203-012-9070-x
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    References listed on IDEAS

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    1. Dzhaparidze, K. & van Zanten, J. H., 2001. "On Bernstein-type inequalities for martingales," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 109-117, May.
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    Cited by:

    1. Herold Dehling & Brice Franke & Jeannette H. C. Woerner, 2017. "Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 1-14, April.

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