A diffusion model with cubic drift: Statistical and computational aspects and application to modelling of the global CO2 emission in Spain

Environmetrics

Volumn 18, Issue 1, 2007, Pages 55-69

  Gutierrez R ^a   Gutierrez Sanchez R ^a   Nafidi, A ^a   Ramos, E ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

CO2 emission in Spain; Cubic drift; Kummer function; Rayleigh and logistic diffusion processes; Simulation; Statistical inference; Trend functions

Indexed keywords

ATMOSPHERIC MODELING; CARBON DIOXIDE; CARBON EMISSION; DIFFUSION; STATISTICAL ANALYSIS; STOCHASTICITY;

EURASIA; EUROPE; SOUTHERN EUROPE; SPAIN;

EID: 33846409857     PISSN: 11804009     EISSN: 1099095X     Source Type: Journal    
DOI: 10.1002/env.801     Document Type: Article

References (33)

1. Andres RJ, Fielding DJ, Marland G, Boden TA, Kumar N. 1999. Carbon dioxide emissions from fossil-fuel use, 1751-1950. Tellus B 51: 759-765.
2. 2 emissions from fossil-fuel burning, hydraulic cement production, and gas flaring: 1950-1992. Technical Report: ORNL/CDIAC-90,NDP-30/R6. Oak Ridge National Laboratory, U.S. Department of Energy: Oak Ridge, Tennessee, USA.
3. Capocelli RM, Ricciardi LM. 1974. A diffusion model for population growth in random environments. Theoretical Population Biology 5(1): 28-41.
4. Chesney M, Elliot J. 1995. Estimating the instantaneous volatility and covariance of risky assets. Applied Stochastic Models and Data Analysis 11: 51-58.
5. Fan J. 2005. A selective overview of nonparametric methods in financial econometrics. Statistical Sciences 20(4): 317-337.
6. Franses PH. 2002. Testing for residual autocorrelation in growth curve models. Technological Forecasting and Social Change 69: 195-204.
7. Gamerman D, Migon HS. 1991. Tractors in Spain - a dynamic reanalysis. Journal of the Operational Research Society 42(2): 119-124.
8. Giorno V, Nobile AG, Ricciardi LM, Sacerdote L. 1986. Some remarks on the Rayleigh process. Journal of Applied Probability 23: 398-408.
9. Golden BL, Zantek PF. 2004. Inaccurate forecasts of the logistic growth model for Nobel prizes. Technological Forecasting and Social Change 71: 417-422.
10. Gradshteyn IS, Ryzhik IM. 1988. Table of Integrals, Series and Products. Academic Press: San Diego.
11. Gutiérrez R, Angulo JM, González A, Pérez R. 1991. Inference in lognormal multidimensional diffusion processes with exogenous factors: application to modelling in Economics. Applied Stochastic Models and Data Analysis 7: 295-316.
12. Gutiérrez R, Ricciardi LM, Román R, Torres P. 1997. First-passage-time densities for time-non-homogeneous diffusion processes. Journal of Applied Probability 34(3): 623-631.
13. Gutiérrez R, Gutiérrez-Sánchez R, Nafidi A, Roman P, Torres F. 2005a. Inference in Gompertz type non-homogeneous stochastic systems by means of discrete sampling. Cybernetics and Systems 36: 203-216.
14. Gutiérrez R, Gutiérrez-Sánchez R, Nafidi A. 2005b. Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model. Applied Energy 80(2): 115-124.
15. Gutiérrez R, Gutiérrez-Sánchez R, Nafidi A. 2006a. Consumption electricity in Morocco: stochastic diffusion analysis with exogenous factors. Applied Energy (in press). Available on line at: www.sciencedirect.com/science/journal/03062619
16. Gutiérrez R, Gutiérrez-Sánchez R, Nafidi A. 2006b. The Stochastic Rayleigh diffusion model: statistical inference and computational aspects. Applications to modelling of real cases. Applied Mathematics and Computation 175: 628-644.
17. Harvey AC. 1984. Time series forecasting based on the logistic curve. Journal of the Operational Research Society 32: 641-646.
18. Kloeden P, Platen E. 1992. The Numerical Solution of Stochastic Differential Equations. Springer: Berlin.
19. Lebedev NN. 1972. Special Functions and Their Applications. Dover publications, Inc: New York.
20. Lipter RS, Shiryayev AN. 1978. Statistics of Random Processes II. Applications. Springer-Verlag: New York.
21. 2 emissions. In Trends: A Compendium of Data on Global Change. Carbon Dioxide Information. Analysis Center/Department of Energy: Oak Ridge National Laboratory, U.S. Oak Ridge, TN, USA.
22. Mar-Molinero C. 1980. Tractors in Spain: a logistic analysis. Journal of the Operational Research Society 31: 141-152.
23. Meade N. 1985. Forecasting using growth curves. An adaptive approach. Journal of Operational Research Society 36(12): 1103-1115.
24. Modis T. 1988. Competition and forecasts for the Nobel prizes awards. Technological Forecasting and Social Change 34(2): 95-102.
25. Nobile AG, Ricciardi LM. 1980. Growth and extinction in random environments. In Application of Information and Control Systems, Lainiotis DG, Tzannes NS (eds). Reidel Pub. Comp.: Dordrecht; 455-465.
26. Nobile AG, Ricciardi LM. 1984a. Growth with regulation in fluctuating environments. Biological Cybernetics 49: 179-188.
27. Nobile AG, Ricciardi LM. 1984b. Growth with regulation in fluctuating environments. II. Intrinsic lower bounds to population size. Biological Cybernetics 50: 285-299.
28. Oliver FM. 1981. Tractors in Spain: a further logistic analysis. Journal of Operational Research Society 32: 499-502.
29. Oliver FM. 1987. A Bayesian model to predict saturation and logistic growth. Journal of Operational Research Society 38: 49-56.
30. Ricciardi LM, Crescenzo A, Giorno V, Nobile AG. 1999. An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling. Mathematical Japonica. 50(2): 247-322.
31. Sepanier J, Oldham KB. 1987. An Atlas of Functions. Springer-Verlag: New York.
32. Skiadas CH, Giovani AN. 1997. A stochastic bass innovation diffusion model for studying the growth of electricity consumption in Greece. Applied Stochastic Models and Data Analysis 13: 85-101.
33. Wong E, Hajek B. 1985. Stochastic Processes in Engineering Systems. Springer-Verlag: New York.