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Contrast estimation for noisy observations of diffusion processes via closed-form density expansions

Abstract : When a continuous-time diffusion is observed only at discrete times with measurement noise, in most cases the transition density is not known and the likelihood is in the form of a high-dimensional integral that does not have a closed-form solution and is difficult to compute accurately. Using Hermite expansions and deconvolution strategy, we provide a general explicit sequence of closed-form contrast for noisy and discretely observed diffusion processes. This work allows the estimation of many diffusion processes. We show that the approximation is very accurate and prove that minimizing the sequence results in a consistent and asymptotically normal estimator. Monte Carlo evidence for the Ornstein-Uhlenbeck process reveals that this method works well and outperforms the Euler expansion of the transition density in situations relevant for financial models.
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https://hal.archives-ouvertes.fr/hal-03374467
Contributor : Fabien Navarro Connect in order to contact the contributor
Submitted on : Tuesday, October 12, 2021 - 10:33:51 AM
Last modification on : Tuesday, October 26, 2021 - 3:58:52 AM

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Salima El Kolei, Fabien Navarro. Contrast estimation for noisy observations of diffusion processes via closed-form density expansions. Statistical Inference for Stochastic Processes, Springer Verlag, 2021, ⟨10.1007/s11203-021-09256-2⟩. ⟨hal-03374467v1⟩

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