Detection, modelling and estimation of non-linear trends by using a non-homogeneous Vasicek stochastic diffusion. Application to CO 2 emissions in Morocco

Stochastic Environmental Research and Risk Assessment

Volumn 26, Issue 4, 2012, Pages 533-543

  Gutierrez R ^a   Gutierrez Sanchez R ^a   Nafidi, A ^b   Pascual, A ^c  

^a UNIVERSITY OF GRANADA   (Spain)

^b HASSAN 1ST UNIVERSITY   (Morocco)

^c UNIVERSITY OF SEVILLE   (Spain)

Author keywords

CO 2 emission in Morocco; Electricity Consumption; Gross Domestic Product; Likelihood estimation; Non homogeneous Vasicek diffusion process; Trend analysis

Indexed keywords

ELECTRICITY CONSUMPTION; GROSS DOMESTIC PRODUCTS; LIKELIHOOD ESTIMATION; NON-HOMOGENEOUS; TREND ANALYSIS;

DIFFUSION; ESTIMATION; PROBABILITY DENSITY FUNCTION; STOCHASTIC SYSTEMS;

CARBON DIOXIDE;

CARBON DIOXIDE; CARBON EMISSION; DETECTION METHOD; ELECTRICITY SUPPLY; ENERGY USE; GROSS DOMESTIC PRODUCT; MAXIMUM LIKELIHOOD ANALYSIS; NUMERICAL MODEL; PROBABILITY DENSITY FUNCTION; STOCHASTICITY; TREND ANALYSIS;

MOROCCO;

EID: 84859439367     PISSN: 14363240     EISSN: 14363259     Source Type: Journal    
DOI: 10.1007/s00477-011-0499-z     Document Type: Article

References (36)

1. Ait-Sahalia Y (1999) Transition densities for interest rate and other nonlinear diffusions. J Finan 54: 1361-1396.
2. Avram F, Leonenko NN, Suvak N (2010) On spectral properties and statistical analysis of Fisher-Snedecor diffusion. arXiv: 1007. 4909v1.
3. Becker S, Germmer M, Jiang T (2006) Spatiotemporal analysis of precipitation trends in the Yangtze River catchment. Stoch Env Res Risk Assess 20(6): 435-444.
4. Black F, Scholes M (1973) The pricing of options and corporate liabilities. Political Econ 81: 637-659.
5. Cantet P, Bacro JN, Arnaud P (2011) Using a rainfall stochastic generator to detect trends in extreme rainfall. Stoch Env Res Risk Assess 25: 429-441.
6. Chan KC, Karolyi GA, Longstaff FA, Sanders AB (1992) An empirical comparison of alternative models of the short-term interest rate. J Finan 3: 1209-1227.
7. Christakos G (2003) Soil behaviour under dynamic loading conditions: experimental procedures and statistical trends. Stoch Env Res Risk Assess 17(3): 175-190.
8. Cox JC (1975) Notes on options pricing I: constant elasticity of variance diffusions. Technical Report, Working paper, Stanford University.
9. Cox J, Ross S (1976) The valuation of options for alternative stochastic processes. J Finan Econ 3: 145-166.
10. Davidov D, Linetsky V (2001) Pricing and hedging path-dependent options under CEV processes. Manag Sci 47(7): 949-965.
11. El-Sharaawi A (1995) Trend detection and estimation with environmental applications. Math Comput Simul 39: 441-447.
12. El-Sharaawi A, Niculescu S (1993) A simple test for detecting non-linear trend. Environmetrics 4: 233-242.
13. Ferrante L, Bompade S, Leone L (2003) A stochastic compartmental model with long lasting infusion. Biom J 45(2): 182-194.
14. Ferrante L, Bompade S, Possati L, Leone L, Montanari MP (2005) A stochastic formulation of the Gompertzian growth model for in vitro bactericidad kinetics: parameter estimation and extinction probability. Biom J 47(3): 306-318.
15. Gutiérrez R, González A, Torres F (1997) Estimation in multivariate lognormal diffusion process with exogenous factors. Appl Stat 4(1): 140-146.
16. Gutiérrez R, Román P, Torres F (1999) Inference and first-passage-time for the lognormal diffusion process with exogenous factors: application to modelling in economics. Appl Stoch Models Bus Ind 15(4): 325-332.
17. Gutiérrez R, Gutiérrez-Sánchez R, Nafidi A (2005a) Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model. Appl Energy 80(2): 115-124.
18. Gutiérrez R, Gutiérrez-Sánchez R, Nafidi A, Román P, Torres F (2005b) Inference in Gompertz type non homogeneous stochastic systems by means of discrete sampling. Cybern Syst 36: 203-216.
19. Gutiérrez R, Gutiérrez-Sánchez R, Nafidi A (2006) Electricity consumption in Morocco: stochastic Gompertz exogenous factors diffusion analysis. Appl Energy 83: 1139-1151.
20. 2 emission in Spain. Environmetrics 18: 55-69.
21. Gutiérrez R, Roldan C, Gutiérrez-Sánchez R, Nafidi A, Angulo JM (2007b) Prediction and conditional simulation of a 2D lognormal diffusion random field. Methodol Comput Appl Prob 9: 413-423.
22. 2 emissions in Spain. Environmetrics 19: 643-658.
23. 2; Kyoto protocol in Spain. Stoch Env Res Risk Assess 22: 55-66.
24. Gutiérrez R, Gutiérrez-Sánchez R, Nafidi A (2009) The trend of the total stock of the private car-petrol in Spain: stochastic modelling using a new Gamma diffusion process. Appl Energy 86: 18-24.
25. Gutiérrez R, Roldan C, Gutiérrez-Sánchez R, Nafidi A, Angulo JM (2010) The effect of nested grid sampling on the parameter estimation of a spatial Gompertz diffusion. Stoch Env Res Risk Assess 24: 539-546.
26. Hull J, White A (1990) Pricing interest-rate derivative securities. Rev Finan Stud 3(4): 573-592.
27. Hunt PJ, Kennedy JE (2000) Financial derivatives in theory and practice. Wiley, New York.
28. Le Maroc en chiffres (1980-2005) Technical Report, Ministère de la Prévision Economique et du Plan, Morocco, Direction de la Statistique.
29. Malliaris AG, Brock WA (1982) Stochastic methods in economics and finance. North-Holland, Amsterdam.
30. Prakasa Rao BSL (1999) Statistical inference for diffusion type process. Arnold/Oxford University Press, London/New York.
31. Shao Q, Li Z, Xu Z (2010) Trend detection in hydrological time series by segment regression with application to Shiyang River Basin. Stoch Env Res Risk Assess 24(2): 221-233.
32. Shoji I, Ozaki T (1996) A statistical comparison of the short-term interest rate models for Japan, US., and Germany. Finan Eng Jpn Mark 3: 263-275.
33. Vasicek OA (1977) An equilibrium characterization of the term structure. J Finan Econ 5: 177-188.
34. Wong E, Hajek B (1985) Stochastic processes in engineering systems. Springer, New York.
35. Xu J, Chen Y, Li W, Yang Y, Hong Y (2011) An integrated statistical approach to identify the nonlinear trend of runoff in the Hotan River and its relations with climatic factors. Stoch Env Res Risk Assess 25: 139-150.
36. Zehna PW (1966) Invariance of maximum likelihood estimators. Ann Math Stat 37: 744.