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

Nafidi, Ahmed; Gutiérrez, Ramón; Gutiérrez-Sánchez, Ramón; Ramos-Ábalos, Eva María; Hachimi, S. El

doi:10.1016/j.energy.2016.07.002

Cited by 17 publications

(7 citation statements)

References 33 publications

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“…An interesting area for future research would be to examine the possibility of defining a non-homogeneous Weibull model, introducing exogenous factors into the drift, similarly to the approach adopted for other diffusions [17,18]. This would enable us to study the factors affecting the evolution of the age dependency ratio for example: fertility, immigration, mortality, health and work ability.…”

Section: Discussionmentioning

confidence: 99%

Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example

et al. 2020

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This paper describes the use of the non-homogeneous stochastic Weibull diffusion process, based on the two-parameter Weibull density function (the trend of which is proportional to the two-parameter Weibull probability density function). The trend function (conditioned and non-conditioned) is analyzed to obtain fits and forecasts for a real data set, taking into account the mean value of the process, the maximum likelihood estimators of the parameters of the model and the computational problems that may arise. To carry out the task, we employ the simulated annealing method for finding the estimators values and achieve the study. Finally, to evaluate the capacity of the model, the study is applied to real modeling data where we discuss the accuracy according to error measures.

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Section: Discussionmentioning

confidence: 99%

Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example

et al. 2020

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“…The substitution of Equations (10) and (11) provides an approximated and asymptotic confidence region of θ and approximated and asymptotic marginal confidence intervals ofα and β. The above-mentioned region is given, for a large T, by:…”

Section: Asymptotic Normality Of Likelihood Estimatorsmentioning

confidence: 99%

“…Diffusion processes are also examined in the field of electricity; in fact, many studies have been focused on the consumption of electrical energy; diverse works suggested a means of using stochastic diffusion processes to model the total consumption of electrical power and to forecast the consumption of electrical energy in relation to particular economic or climatologic variables, using statistical techniques. In this respect, see the works of Gutiérrez et al, who proposed a means of using stochastic diffusion processes to model the total consumption of electrical power in Morocco [10], and Nafidi et al, who modeled electric power consumption throughout a period of economic crisis [11].…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

2019

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In this paper, we study the one-dimensional homogeneous stochastic Brennan–Schwartz diffusion process. This model is a generalization of the homogeneous lognormal diffusion process. What is more, it is used in various contexts of financial mathematics, for example in deriving a numerical model for convertible bond prices. In this work, we obtain the probabilistic characteristics of the process such as the analytical expression, the trend functions (conditional and non-conditional), and the stationary distribution of the model. We also establish a methodology for the estimation of the parameters in the process: First, we estimate the drift parameters by the maximum likelihood approach, with continuous sampling. Then, we estimate the diffusion coefficient by a numerical approximation. Finally, to evaluate the capability of this process for modeling real data, we applied the stochastic Brennan–Schwartz diffusion process to study the evolution of electricity net consumption in Morocco.

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“…In contrast observations from many fields such a as neuroscience, finance and biology, suggest otherwise. Various non-homogeneous SDPs have been proposed to reflect this time dependent behavior, see for example: Lognormal [9], Gompertz [10], Vasicek [11], Brennan-Schwartz [12], and Gamma [13] processes.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Lomax Diffusion Process: Statistical Inference and Application

2021

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In this paper, we discuss a new stochastic diffusion process in which the trend function is proportional to the Lomax density function. This distribution arises naturally in the studies of the frequency of extremely rare events. We first consider the probabilistic characteristics of the proposed model, including its analytic expression as the unique solution to a stochastic differential equation, the transition probability density function together with the conditional and unconditional trend functions. Then, we present a method to address the problem of parameter estimation using maximum likelihood with discrete sampling. This estimation requires the solution of a non-linear equation, which is achieved via the simulated annealing method. Finally, we apply the proposed model to a real-world example concerning adolescent fertility rate in Morocco.

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

Cited by 17 publications

References 33 publications

Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example

Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example

Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

A Stochastic Lomax Diffusion Process: Statistical Inference and Application

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