A Vasicek-Type Model with Structural Breaks in the Drift

We consider a time inhomogeneous diffusion process with piece-wise linear drift and infinitesimal variance generally depending on time. Such a process is able to model the dynamics of phenomena in which structural breaks occur at fixed times due to sudden changes. The probability distribution of such process is analyzed by obtaining its transition probability density function and the related moments. Moreover, we focus on the statistical analysis of the process. In par- ticular, starting from a discrete sampling, an inference procedure based on the maximum likelihood estimation and the generalized method of moments is provided to address the estimation of the drift and of the infinitesimal variance. Finally, a simulation study is made to evaluate the performance of the provided procedure. In such simulation study, by means of a suitable statistical test we also discuss the presence of structural breaks in the drift parameters.