A τ-power stochastic gamma diffusion process: Computational statistical inference and simulation aspects. A real example

In this paper, we model the pattern of natural-gas consumption in Spain, using a new stochastic τ-power gamma diffusion process, defined from a non-homogeneous gamma diffusion process. We study the probabilistic characteristics derived from the corresponding Ito stochastic differential equation and obtain the trend functions. We present a computational approach to the statistical fitting of the process and analyse the stochastic simulation of its trajectories. The probabilistic and statistical results obtained are applied to modelling the above mentioned random phenomenon, using real annual consumption data observed for the period (1985–2010). We conclude that the proposed diffusion model, with a given value of the power τ, is appropriate for the task discussed.