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Stochastic Square of the Brennan-Schwartz Diffusion Process: Statistical Computation and Application

Author

Listed:
  • Ahmed Nafidi

    (LAMSAD, École Nationale des Sciences Appliquées de Berrechid)

  • Ghizlane Moutabir

    (LAMSAD, École Nationale des Sciences Appliquées de Berrechid)

  • Ramón Gutiérrez-Sánchez

    (University of Granada)

  • Eva Ramos-Ábalos

    (University of Granada)

Abstract

In this paper, we study a new one-dimensional homogeneous stochastic process, termed the Square of the Brennan-Schwartz model, which is used in various contexts. We first establish the probabilistic characteristics of the model, such as the analytical expression solution to Itô’s stochastic differential equation, after which we determine the trend functions (conditional and non-conditional) and the likelihood approach in order to estimate the parameters in the drift. Then, in the diffusion coefficient, we consider the problem of parameter estimation, doing so by a numerical approximation. Finally, we present an application to population growth by the use of real data, namely the growth of the total population aged 65 and over, resident in the Arab Maghreb, to illustrate the research methodology presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09714-8
    DOI: 10.1007/s11009-019-09714-8
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    References listed on IDEAS

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    Cited by:

    1. Ahmed Nafidi & Abdenbi El Azri & Ramón Gutiérrez-Sánchez, 2023. "A Stochastic Schumacher Diffusion Process: Probability Characteristics Computation and Statistical Analysis," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-15, June.

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