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A stochastic Bass innovation diffusion model for studying the growth of electricity consumption in Greece

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  • C. H. Skiadas
  • A. N. Giovanis

Abstract

In this paper a stochastic innovation diffusion model is proposed derived by introducing stochasticity into the well‐known Bass model. The stochastic model is solved analytically by using the theory of reducible stochastic differential equations and the first moment of the resulting stochastic process is presented. The parameter estimators of the model are derived by using a procedure which provides the maximum likelihood estimators (MLE) using time series data. Finally, the model is applied to the data of electricity consumption in Greece. Using a simulation technique, it is possible to predict the performance of the consumption process by defining a subdomain to which all possible trajectories of the process should belong with a predefined probability. © 1997 by John Wiley & Sons, Ltd.

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  • C. H. Skiadas & A. N. Giovanis, 1997. "A stochastic Bass innovation diffusion model for studying the growth of electricity consumption in Greece," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(2), pages 85-101, June.
    • Handle: RePEc:wly:apsmda:v:13:y:1997:i:2:p:85-101
    DOI: 10.1002/(SICI)1099-0747(199706)13:23.0.CO;2-Z
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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. Michalakelis, C. & Sphicopoulos, T., 2012. "A population dependent diffusion model with a stochastic extension," International Journal of Forecasting, Elsevier, vol. 28(3), pages 587-606.
    3. Eryn Juan He & Joel Goh, 2022. "Profit or Growth? Dynamic Order Allocation in a Hybrid Workforce," Management Science, INFORMS, vol. 68(8), pages 5891-5906, August.
    4. Shun-Chen Niu, 2006. "A Piecewise-Diffusion Model of New-Product Demands," Operations Research, INFORMS, vol. 54(4), pages 678-695, August.
    5. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez & Eva Ramos-Ábalos, 2020. "Stochastic Square of the Brennan-Schwartz Diffusion Process: Statistical Computation and Application," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 455-476, June.
    6. A. Negahban & J.S. Smith, 2016. "The effect of supply and demand uncertainties on the optimal production and sales plans for new products," International Journal of Production Research, Taylor & Francis Journals, vol. 54(13), pages 3852-3869, July.
    7. Eva María Ramos-Ábalos & Ramón Gutiérrez-Sánchez & Ahmed Nafidi, 2020. "Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    8. Wenjing Shen & Izak Duenyas & Roman Kapuscinski, 2014. "Optimal Pricing, Production, and Inventory for New Product Diffusion Under Supply Constraints," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 28-45, February.
    9. Christos H. Skiadas, 2010. "Exact Solutions of Stochastic Differential Equations: Gompertz, Generalized Logistic and Revised Exponential," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 261-270, June.
    10. 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.

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