Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Threshold diffusions are regime-switching continuous-time models where the model switches between two or more different model behaviors as the state variable cross certain domains.  We consider the statistical estimation on the switching threshold value for a discretely observed one-dimensional diffusion process. Specifically, in our situation, the drift coefficient of the diffusion process is discontinuous in the threshold parameter which introduces technical problems because of the lack of regularity of the transition density. We present a  moment estimator and a quasi-likelihood estimator and compare their performance.