Prediction-based Estimating Functions for Diffusion Processes with Measurement Noise

The prediction-based estimating functions proposed by (Sørensen, 1999) are generalized to facilitate parameter estimation in discretely observed stochastic differential equations, where the observations are corrupted by additive white noise. The new class of estimating functions has most of the nice properties of martingale estimating functions. However, they may be applied when no obvious or easily calculated martingales exist. Simple expressions are derived for the optimal estimating functions when the classes of generalized prediction-based estimating functions are defined by a finite-dimensional space of predictors. Only unconditional moments are needed for this class of estimating functions, so a considerably smaller amount of simulation is needed compared to other classes of estimating functions based on conditional moments. Particular attention is devoted to the Cox-Ingersoll-Ross model and stochastic volatility models. Using Monte Carlo simulation the smallsample properties are examined and the method is compared to other estimating functions.