Application of Stochastic Lognormal Diffusion Model with Polynomial Exogenous Factors to Energy Consumption in Ghana

Abstract

The main objective of this paper was the application of maximum likelihood ratio tests in lognormal diffusions with polynomial exogenous factors. The model described an innovation diffusion process considering at the same time disturbances coming from the environment of the system. Finally, the model was applied to energy consumption data in Ghana from 1999 to 2010.

Maximum likelihood estimators (MLEs) were obtained for the drift and diffusion coefficients characterizing lognormal diffusion models involving exogenous factors affecting the drift term. The present paper provides the distribution of these MLEs, the Fisher information matrix, and the solution to some likelihood ratio tests of interest for hypotheses on the parameters weighting the relative effect of the exogenous factors.

The results show that the total consumption of primary energy presents structural characteristics. The endogenous consumption pattern in Ghana, in absolute terms, also presents a clear upward trend.

Key works: lognormal diffusions model, maximum likelihood estimators, endogenous actors, energy consumption