Infinitesimal Robustness for Diffusions

We develop infinitesimally robust statistical procedures for general diffusion processes. We first prove existence and uniqueness of the times series influence function of conditionally unbiased M–estimators for ergodic and stationary dffusions, under weak conditions on the (martingale) estimating function used. We then characterize the robustness of M–estimators for diffusions and derive a class of conditionally unbiased optimal robust estimators. To compute these estimators, we propose a general algorithm, which exploits approximation methods for dffusions in the computation of the robust estimating function. Monte Carlo simulation shows a good performance of our robust estimators and an application to the robust estimation of the exchange rate dynamics within a target zone illustrates the methodology in a real–data application.