Trend analysis using nonhomogeneous stochastic diffusion processes. Emission of CO2; Kyoto protocol in Spain

Original Paper

DOI: 10.1007/s00477-006-0097-7

Cite this article as:
Gutiérrez, R., Gutiérrez-Sánchez, R. & Nafidi, A. Stoch Environ Res Risk Assess (2008) 22: 57. doi:10.1007/s00477-006-0097-7


In this study, we propose a methodology to analyse the gradual secular trends present in the time evolution of certain endogenous variables, which are of particular interest in environmental research. This methodology is based on modelling such variables by nonhomogeneous stochastic diffusion processes, the trend functions of which may be made to depend on other, exogenous, variables, which are controllable and which affect and model, in turn, the possible irregularities of such trends. The methodology is applied to analyse the evolution of the emission of CO2 in Spain, and it is shown that the evolution of the Spanish GDP affects the trend component. These circumstances are considered in the context of Spain’s non-compliance with the Kyoto protocol on controlling the emission of greenhouse gases.


Non-homogeneous lognormal and Gompertz diffusion process Exogenous factors Trend functions Likelihood estimation in discrete sampling GDP and global CO2 emission 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • R. Gutiérrez
    • 1
  • R. Gutiérrez-Sánchez
    • 1
  • A. Nafidi
    • 1
  1. 1.Department of Statistics and Operations Research, Facultad de CienciasUniversity of GranadaGranadaSpain

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