Estimating the parameters of stochastic differential equations by Monte Carlo methods

We propose a method for the simultaneous estimation of the drift and diffusion coefficients of stochastic differential equations (SDE) from panel data. The method involves matching the distribution of the experimental/field data with a panel of simulated data generated by a Monte Carlo experiment. The fit between the two distributions is assessed by means of the chi-square goodness-of-fit statistic leading to a confidence function computed from an incomplete gamma function. A numerical optimisation algorithm then optimises the choice of parameters to maximise this function. Preliminary evidence is presented which suggests that it is possible to estimate the coefficients of the generating SDE very accurately.