A bivariate stochastic Gamma diffusion model: statistical inference and application to the joint modelling of the gross domestic product and CO2 emissions in Spain

This paper examines the use of a bivariate stochastic Gamma diffusion model to represent the co-evolution of the stochastic variables CO2 emission and gross domestic product (GDP) in Spain. These variables were selected in view of the strong correlation between them. We compare the results obtained to those provided by the Gamma one-dimensional process with exogenous factors, taking CO2 emission as an endogenous variable and GDP as the exogenous factor. This methodology was applied to a real case, with two dependent variables: firstly, GDP and CO2 emission from the combustion of fossil fuels (gas, liquid and solid fuels) and cement manufacture in Spain. And secondly, with GDP and CO2 emission from the consumption and flaring of natural gas in Spain. The joint dynamic evolution of these factors is represented by the proposed model. In addition, a comparison is made with results obtained from fitting the data using the Gamma diffusion process with external factors, in which GDP is the variable containing the external information. This implementation was carried out on the basis of annual observations of the variables over the periods 1986–2008 and 1986–2009, respectively.