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Indirect Robust Inference with Application to Diffusion Models

In complex statistical models, like diffusion models described by stochastic differential equations (SDE), it is often difficult or impossible to carry out standard likelihood based estimation and inference. Diffusion models play an important role in finance, e.g. when estimating the short-term interest rate process. Typically the estimation of a diffusion model is performed using an auxiliary discretized model which is easier to estimate then the original SDE. It is well known that estimators based on a discretization of the diffusion model are biased. An additional problem that arises when estimating the short-term interest rate process is the possible model misspecification which can lead to biased estimators and misleading test results. In this work, we introduce the Indirect Robust Generalized Method of Moments (IRGMM), a new simulation-based estimation of diffusion models. The primary advantage of IRGMM relative to classical estimators of continuous-time diffusion processes is that it corrects both the errors due to discretization and the errors due to model misspecification. We apply this approach to monthly US risk free rates and to various monthly Eurocurrency rates and provide extensive evidence of its predictive performances in a variety of settings.