Stochastic modeling with time-inhomogeneous Jacobi diffusions: applications to bounded and seasonal environmental processes

In this paper we explore stochastic modeling of bounded processes in continuous time using time-inhomogeneous Jacobi diffusions. We present some basic general results and introduce a subclass of models with seasonal time variation. In the seasonal models we derive the conditional mean and variance in closed form and propose a strategy for estimation based on quasi maximum likelihood. An empirical application is carried out to daily time series data on relative humidity. Simulation methods are used to investigate properties of the resulting parameter estimators. The results show that the proposed seasonal Jacobi model gives a very satisfactory fit to data and that the estimation procedure works well.