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The trend of the total stock of the private car-petrol in Spain: Stochastic modelling using a new gamma diffusion process


  • Gutiérrez, R.
  • Gutiérrez-Sánchez, R.
  • Nafidi, A.


The main aim of this study is to model the trend of the evolution of the total stock of private petrol-driven cars. In Spain, as in other EU countries, this trend between 2000 and 2005 differed significantly from that observed from 1986 to 1999. Moreover, it varies greatly from that corresponding to the stock of diesel-driven cars, which consistently presents an exponential Gompertz-type increase. Spain constitutes a typical example of a failure to observe the maximum CO2 emission levels assigned to it by 2012 under the Kyoto Protocol (1992); a significant percentage of these excess emissions is accounted for by the land transport sector, in general, and by the private cars subsector, in particular. This paper proposes a stochastic model based on a new non homogeneous stochastic gamma-type diffusion process which it is a stochastic version of a Gamma function type deterministic growth model considered in Skiadas [1]. We describe its main probabilistic characteristics and establish a statistical methodology by which it can be fitted to real data and obtain medium-term forecasts that, in statistical terms, are quite accurate.

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  • 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," Applied Energy, Elsevier, pages 18-24.
  • Handle: RePEc:eee:appene:v:86:y:2009:i:1:p:18-24

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    References listed on IDEAS

    1. Manuel Arapis & Jiti Gao, 2006. "Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 310-345.
    2. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2006. "Electricity consumption in Morocco: Stochastic Gompertz diffusion analysis with exogenous factors," Applied Energy, Elsevier, vol. 83(10), pages 1139-1151, October.
    3. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, pages 297-316.
    4. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, pages 223-262.
    5. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    6. Gutiérrez, R. & Nafidi, A. & Gutiérrez Sánchez, R., 2005. "Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model," Applied Energy, Elsevier, vol. 80(2), pages 115-124, February.
    7. Ramón Gutiérrez & Patrica Román & Francisco Torres, 2001. "Inference on some parametric functions in the univeriate lognormal diffusion process with exogenous factors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 357-373, December.
    8. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Reply," Journal of Business & Economic Statistics, American Statistical Association, pages 335-338.
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    Cited by:

    1. Gutiérrez-Sánchez, R. & Nafidi, A. & Pascual, A. & Ramos-Ábalos, E., 2011. "Three parameter gamma-type growth curve, using a stochastic gamma diffusion model: Computational statistical aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 234-243.
    2. Forouzanfar, Mehdi & Doustmohammadi, A. & Hasanzadeh, Samira & Shakouri G, H., 2012. "Transport energy demand forecast using multi-level genetic programming," Applied Energy, Elsevier, vol. 91(1), pages 496-503.
    3. Nafidi, A. & Gutiérrez, R. & Gutiérrez-Sánchez, R. & Ramos-Ábalos, E. & El Hachimi, S., 2016. "Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors," Energy, Elsevier, vol. 113(C), pages 309-318.


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