Forecasting a class of doubly stochastic Poisson processes

This paper deals with the doubly stochastic Poisson process (DSPP) with mean a truncated Gaussian distribution at any instant of time. The expression of its probability mass function is derived in this paper and it is also proved that the value of the process with maximum probability can be found in a known bounded interval. Furthermore, this paper also presents two methods to forecast the evolution of this kind of DSPP. The first one consists in modelling the mean process and then the probability mass function of the DSPP. The second method uses Multivariate Principal Component Regression to forecast the sample mean in the future instant and then the mass function. Both methods are applied to the real process of number of unpaid bank bills in Spain, forecasting the mass function of this process in 1997 and also its mode.