Grey Lotka–Volterra models with application to cryptocurrencies adoption

Gatabazi, Paul; Pindza, Edson; Labuschagne, Coenraad C.A.

doi:10.1016/j.chaos.2019.03.006

Cited by 49 publications

(21 citation statements)

References 25 publications

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“…Remark 2 shows that the unified model can yield the high-dimensional system that are employed to describe interactions between species and, additionally, if d = 2, then the unified model is actually the classical grey Lotka-Volterra model [13]. Furthermore, similar to the expansions in Remark 1, the unified model could deduce some other novel multi-output models.…”

Section: Unified Framework For Nonlinear Grey System Modelsmentioning

confidence: 76%

“…sions, in particular, KRNGM(1,n) uses kernel tricks to introduce other variables. Further ones lead to grey output models, but to our knowledge, research of multi-output models is sparse and mainly focused on the grey prey-predator system (GLVM(1,2)) concerning accuracy improvement [38,19] and stability analysis [13,32].…”

Section: Extended Nonlinear Grey System Modelsmentioning

confidence: 99%

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On unified framework for nonlinear grey system models: an integro-differential equation perspective

Yang,

Xie,

Wei

et al. 2021

Preprint

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Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models and developing novel models, relatively limited attention has been paid to the relationship among diverse models and the modelling mechanism. The current paper proposes a unified framework and reconstructs the unified model from an integro-differential equation perspective. First, we propose a methodological framework that subsumes various nonlinear grey system models as special cases, providing a cumulative sum series-orientated modelling paradigm. Then, by introducing an integral operator, the unified model is reduced to an equivalent integro-differential equation; on this basis, the structural parameters and initial value are estimated simultaneously via the integral matching approach. The modelling procedure comparison further indicates that the integral matching-based integro-differential equation provides a direct modelling paradigm. Next, large-scale Monte Carlo simulations are conducted to compare the finite sample performance, and the results show that the reduced model has higher accuracy and robustness to noise. Applications of forecasting the municipal sewage discharge and water consumption in the Yangtze River Delta of China further illustrate the effectiveness of the reconstructed nonlinear grey models.

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Section: Unified Framework For Nonlinear Grey System Modelsmentioning

confidence: 76%

Section: Extended Nonlinear Grey System Modelsmentioning

confidence: 99%

On unified framework for nonlinear grey system models: an integro-differential equation perspective

Yang,

Xie,

Wei

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…3. Calculate the error and use it if the accuracy meets the requirements according to (9) to (11); otherwise, establish a residual sequence ε (0) in accordance with (13). Use the residual GM method if the residual tail segment modeling condition is met.…”

Section: Residual Gm Network Model Based On Bp-pemea Correctionmentioning

confidence: 99%

Research on residual GM optimization based on PEMEA-BP correction

Duan

Zhu

Wei

et al. 2020

Sci Rep

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With the advantages of small samples and high accuracy, Grey Model (GM) still has two major problems need to be addressed, high input data requirements and large margin of error. Hence, this paper proposes an algorithm based on Populational Entropy Based Mind Evolutionary Algorithm-Error Back Propagation Training Artificial Neural Algorithm to modify GM residual tail, which will not only keep the advantages of GM, but also expand its scope of use to various non-linear and even multidimensional objects. Meanwhile, it can avoid defects of other algorithms, such as slow convergence and easy to fall into the local minimum. In small samples data experiments, judging from SSE, MAE, MSE, MAPE, MRE and other indicators, this new algorithm has significant advantage over GM, BP algorithm and combined genetic algorithm in terms of simulation accuracy and convergence speed.

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“…Grey prediction model is the core component of the grey system theory, and its main models, such as the classical grey model GM(1,1) [1], multivariable grey model GM(1, N) [2], grey Verhulst model [3,4], grey Bernoulli model [5], have made some progress. These models have been successfully applied to fields such as energy [6], finance [7] and mechanical [8], etc. The multivariate grey model has attracted the attention of scholars because it can better reflect the mutual influence and restriction among variables in the system.…”

Section: Introductionmentioning

confidence: 99%

Fractional derivative multivariable grey model for nonstationary sequence and its application

Kang

Mao

Zhang

et al. 2020

J. of Syst. Eng. Electron.

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Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization (PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste (MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.

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Grey Lotka–Volterra models with application to cryptocurrencies adoption

Cited by 49 publications

References 25 publications

On unified framework for nonlinear grey system models: an integro-differential equation perspective

On unified framework for nonlinear grey system models: an integro-differential equation perspective

Research on residual GM optimization based on PEMEA-BP correction

Fractional derivative multivariable grey model for nonstationary sequence and its application

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