Parameter Estimation for a Discretely Observed Integrated Diffusion Process

Arnaud Gloter

Scandinavian Journal of Statistics, 2006, vol. 33, issue 1, 83-104

Abstract: 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 iΔ,i = 1,…,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.

Date: 2006
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https://doi.org/10.1111/j.1467-9469.2006.00465.x

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