Trend analysis and computational statistical estimation in a stochastic Rayleigh model: Simulation and application

This paper considers a stochastic model based on the homogeneous stochastic Rayleigh diffusion process. We first examine the main probabilistic characteristics of the model and describe, among other results, an explicit expression of the trends (both conditioned and nonconditioned) and, when it exists, the stationary distribution. We then obtain results of the statistical estimation of the corresponding parameters and consider the computational problems that may arise. In addition, we present an algorithm for the stochastic simulation of the sample path of the model based on the corresponding Ito stochastic differential equation. Finally, the model is applied to study the evolution of the production of thermal electricity in countries in the Maghreb region; the results obtained are in good statistical accord with the real data observed for the period 1980–2002