Indirect Inference for Stochastic Differential Equations Based on Moment Expansions

Abstract

We provide an indirect inference method to estimate the parameters of timehomogeneous scalar diffusion and jump diffusion processes. We obtain a system of ODEs that approximate the time evolution of the first two moments of the process by the approximation of the stochastic model applying a second order Taylor expansion of the SDE s infinitesimal generator in the Dynkin s formula. This method allows a simple and efficient procedure to infer the parameters of such stochastic processes given the data by the maximization of the likelihood of an approximating Gaussian process described by the two moments equations. Finally, we perform numerical experiments for two datasets arising from organic and inorganic fouling deposition phenomena.