Stochastic diffusion process based on Goel-Okumoto curve: statistical inference and application to real data

In this paper we study a new stochastic diffusion process based on the Goel-Okumoto curve. Such a process can be considered as an extension of the nonhomogeneous lognormal diffusion process. From the corresponding Ito's stochastic differential equation (SDE), firstly we establish the probabilistic characteristics of the studied process, such as the solution to the SDE, the probability transition density function and their distribution, the moments function, in particular the conditional and non-conditional trend functions. Secondly, we treat the parameters estimation problem by using the maximum likelihood method in basis of the discrete sampling, thus we obtain nonlinear equations that can be solved by numerical methods. Finally, the proposed model is applied to the data of the broad money (% GDP) of Morocco.