Stochastic gamma diffusion process with exogenous factors. Application to real case

摘要

The principal objective of the present work is to study a new extension of the one-dimensional stochastic gamma diffusion process by introducing external time functions as exogenous factors. This original process can be used profitably in a variety of disciplines including Biology, Geology, Agriculture, Environmetrics and Population Dynamics. Firstly, we determine the probabilistic characteristics of the studied process as the analytical expression of the process, its transition probability density function and their trend functions. Secondly, we study the statistical inference in this process: we estimate the parameters present in the model by using the maximum likelihood estimation method in basis of the discrete sampling of the process, thus obtaining the expression of the likelihood estimators. Finally, we applied this methodology to the real case, Gross Domestic Product (GDP) and CO2 emissions from the consumption and flaring of natural gas in Spain. This implementation is carried out on the basis of annual observations of the variables over the period 1986-2009.