Parameter Estimation from Occupation Times
This provides a new estimation method for Ornstein-Uhlenbeck parameters when only occupation times are observed, which is relevant for applications in finance and physics.
The authors derive an equation for the expected occupation time of the centered Ornstein-Uhlenbeck process, enabling parameter estimation via least squares minimization. In Monte Carlo simulations, the method successfully recovers the true parameters.
We derive an equation to compute directly the expected occupation time of the centered Ornstein-Uhlenbeck process. This allows us to identify the parameters of the Ornstein-Uhlenbeck process for available occupation times via a standard least squares minimization. To test the method, we generate occupation times via Monte-Carlo simulations and recover the parameters with the above mentioned procedure.