A τ-power stochastic gamma diffusion process: Computational statistical inference and simulation aspects. A real example

Jáimez, Ramón Gutiérrez; Gutiérrez-Sánchez, Ramón; Nafidi, Ahmed; Ramos-Ábalos, Eva María

doi:10.1016/j.amc.2012.07.058

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…Let {X(t); t ∈ [t 0 , T]; t 0 ≥ 0} be a stochastic process taking values on (0, ∞), X(t) is a Gompertz diffusion process with parameters α, β and σ and which is denoted by Gomp(α; β; σ) if X(t) satisfies Ito's Stochastic Differential Equation (SDE) as follows (see [16,18,20,37]):…”

Section: An Overview Of the Homogeneous Gompertz Stochastic Diffusionmentioning

confidence: 99%

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Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation

2020

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In this paper, we study a new family of Gompertz processes, defined by the power of the homogeneous Gompertz diffusion process, which we term the powers of the stochastic Gompertz diffusion process. First, we show that this homogenous Gompertz diffusion process is stable, by power transformation, and determine the probabilistic characteristics of the process, i.e., its analytic expression, the transition probability density function and the trend functions. We then study the statistical inference in this process. The parameters present in the model are studied by using the maximum likelihood estimation method, based on discrete sampling, thus obtaining the expression of the likelihood estimators and their ergodic properties. We then obtain the power process of the stochastic lognormal diffusion as the limit of the Gompertz process being studied and go on to obtain all the probabilistic characteristics and the statistical inference. Finally, the proposed model is applied to simulated data. both in the homogeneous and in the non-homogeneous cases and many particular SDP have been proposed, such as Katsamaki and Skiadas [11] in the case of the exponential model, Skiadas and Giovanis [12] in the case of the Bass model, Giovanis and Skiadas [13] in the case of the logistic model, Gutiérrez et al. [14] in the case of the Rayleigh model and in the case of the lognormal with exogenous factors.Among the above-mentioned processes is the Stochastic Gompertz Diffusion Process (SGDP), which was first proposed by Ricciardi [16], who defined it in the homogeneous case by means of stochastic differential equations, for use in studies of population growth. It was subsequently used by Dennis and Patil [17] in ecology modelling. With respect to the Kolmogorov equations, it was defined by Nafidi [18], in a general way and for both the univariate and the multivariate cases. In various papers, Gutiérrez et al. [19-21], Ferrante et al. [22], Román-Román et al. [23] and Giorno and Nobile [24], have highlighted the importance of this process, and many subsequent extensions have appeared, especially regarding the non-homogeneous case with exogenous factors (external variables) that affect the drift coefficient. In general, these extensions take one of the following two forms:With external information (when no functional form is available): the exogenous factors are completely determined by the observed data (monthly, annual, etc.) and to obtain their functional forms interpolation methods, among others, can be used. This methodology has been applied by Gutiérrez et al. [25,26], Rupsys et al. [27] and Badurally Adam et al. [28]. In all these papers it is assumed that the coefficient drift is a linear combination of exogenous factors, obtained by linear interpolation.Without external information: in this case there are no observed data for the exogenous factors, but they are functions of time and of certain parameters. For example, the case in which the deceleration factor is affected by exogenous factors was developed by Gutiérrez et a...

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Section: An Overview Of the Homogeneous Gompertz Stochastic Diffusionmentioning

confidence: 99%

“…The analytical expression of the unique solution to Equation (1) is given by (see, for example, [21,37])…”

Section: An Overview Of the Homogeneous Gompertz Stochastic Diffusionmentioning

confidence: 99%

Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation

2020

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Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors

Nafidi

Gutiérrez

Gutiérrez-Sánchez

et al. 2016

Energy

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A γ-power stochastic Lundqvist-Korf diffusion process: Computational aspects and simulation

Abdenbi

Nafidi

2022

Moroccan Journal of Pure and Applied Analysis

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In this paper, we introduce a new family of stochastic Lundqvist-Korf diffusion process, defined from a g-power of the Lundqvist-Korf diffusion process. First, we determine the probabilistic characteristics of the process, such as its analytic expression, the transition probability density function from the corresponding It ˆo stochastic differential equation and obtain the conditional and non-conditional mean functions. We then study the statistical inference in this process. The parameters of this process are estimated by using the maximum likelihood estimation method with discrete sampling, thus we obtain a nonlinear equation, which is achieved via the simulated annealing algorithm. Finally, the results of the paper are applied to simulated data.

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A τ-power stochastic gamma diffusion process: Computational statistical inference and simulation aspects. A real example

Cited by 3 publications

References 12 publications

Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation

Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation

Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors

A γ-power stochastic Lundqvist-Korf diffusion process: Computational aspects and simulation

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