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

Ahmed Nafidi, Ghizlane Moutabir (), Ramón Gutiérrez-Sánchez and Eva Ramos-Ábalos
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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

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 2, 455-476

Abstract: 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.

Keywords: Brennan Schwartz diffusion Process; Stochastic differential equation; Statistical inference in diffusion process; Stationary distribution; Trend function; Application to population growth; 62M86; 60H30; 65C30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09714-8

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