Efficient computation of the quasi likelihood function for discretely observed diffusion processes

An efficient numerical method for nearly simultaneous computation of all conditional moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations is presented. The method is not restricted to any particular dynamics of the stochastic differential equation and is virtually insensitive to the sampling interval. The key contribution is that computational complexity is sublinear in terms of expensive operations in the number of observations as all moments can be computed offline in a single operation. Simulations show that the bias of the method is small compared to the random error in the estimates, and to the bias of comparable methods. Furthermore the computational cost is comparable (actually faster for moderate and large data sets) to the simple, but in some applications badly biased, the Euler–Maruyama approximation.