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Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain

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  • R. Gutiérrez
  • R. Gutiérrez‐Sánchez
  • A. Nafidi

Abstract

In the present study, we treat the stochastic homogeneous Gompertz diffusion process (SHGDP) by the approach of the Kolmogorov equation. Firstly, using a transformation in diffusion processes, we show that the probability transition density function of this process has a lognormal time‐dependent distribution, from which the trend and conditional trend functions and the stationary distribution are obtained. Second, the maximum likelihood approach is adapted to the problem of parameters estimation in the drift and the diffusion coefficient using discrete sampling of the process, then the approximated asymptotic confidence intervals of the parameter are obtained. Later, we obtain the corresponding inference of the stochastic homogeneous lognormal diffusion process as limit from the inference of SHGDP when the deceleration factor tends to zero. A statistical methodology, based on the above results, is proposed for trend analysis. Such a methodology is applied to modelling and forecasting vehicle stocks. Finally, an application is given to illustrate the methodology presented using real data, concretely the total vehicle stocks in Spain. Copyright © 2008 John Wiley & Sons, Ltd.

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  • R. Gutiérrez & R. Gutiérrez‐Sánchez & A. Nafidi, 2009. "Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 385-405, May.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:3:p:385-405
    DOI: 10.1002/asmb.754
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    References listed on IDEAS

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    Cited by:

    1. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    2. Le Boulzec, Hugo & Delannoy, Louis & Andrieu, Baptiste & Verzier, François & Vidal, Olivier & Mathy, Sandrine, 2022. "Dynamic modeling of global fossil fuel infrastructure and materials needs: Overcoming a lack of available data," Applied Energy, Elsevier, vol. 326(C).
    3. Ahmed Nafidi & Ilyasse Makroz & Ramón Gutiérrez Sánchez, 2021. "A Stochastic Lomax Diffusion Process: Statistical Inference and Application," Mathematics, MDPI, vol. 9(1), pages 1-9, January.
    4. Nafidi, Ahmed & El Azri, Abdenbi, 2021. "A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 25-38.

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