Fractional-Order Grey Prediction Method for Non-Equidistant Sequences

Shen, Yue; He, Bo; Qin, Ping

doi:10.3390/e18060227

Cited by 11 publications

(3 citation statements)

References 18 publications

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“…In addition, the fractional order reducing generation sequence of X (0) (k) was defined by [22] and a negative fractional order accumulated operation was introduced by [26].…”

Section: The Conformable Fractional Accumulation and Differencementioning

confidence: 99%

An optimized continuous fractional grey model for forecasting of the time dependent real world cases

Öztürk

Bilgil

Erdinç

2022

Hacettepe Journal of Mathematics and Statistics

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The new priority in the grey modelling is to build new models that have more accurate forecasting power than the previous ones. This paper aims to develop the prediction performance of the existing continuous grey models. Therefore, a novel continuous grey model (OCCFGM(1,1)) is proposed with conformable fractional derivative. The numerical results of three case studies show that the novel model's prediction accuracy is higher than other competitive models, and the proposed model is more reasonable for practical cases.

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“…In addition, the fractional order reducing generation sequence of X (0) (k) was defined by [22] and a negative fractional order accumulated operation was introduced by [26].…”

Section: The Conformable Fractional Accumulation and Differencementioning

confidence: 99%

An optimized continuous fractional grey model for forecasting of the time dependent real world cases

Öztürk

Bilgil

Erdinç

2022

Hacettepe Journal of Mathematics and Statistics

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“…Fractional order accumulation is a new accumulating method based on a principle of the new information priority, which has been widely used in the grey prediction model (Wu et al, 2013;Wu et al, 2015;Liu et al, 2015;Mao et al, 2015;Meng et al, 2016;Yang and Zhao, 2015;Shen et al, 2016). The research shows that the accuracy of grey model can reach its highest value by selecting a reasonable order.…”

Section: Introductionmentioning

confidence: 99%

Analysing the high-tech industry with a multivariable grey forecasting model based on fractional order accumulation

Zeng¹

2019

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Purpose High-tech industries play an important role in promoting economic and social development. The purpose of this paper is to accurately predict and analyze the output value of high-tech products in Guangdong Province, China, by using a multivariable grey model. Design/methodology/approach Based on the principle of fractional order accumulation, this study proposes a multivariable grey prediction model. To further enhance the prediction ability and accuracy of the model, an optimized model is established by reconstructing the background value. The optimal parameters are solved by minimizing the average relative error of the system characteristic sequence with the constraint of parameter relationships. Findings The results from the study show that the two proposed models exhibit better simulation and prediction performance than the traditional models, while the optimized model can significantly improve the modelling precision. In addition, it is predicted that the output value of high-tech products is 12,269.443bn yuan in 2021, which will approximately double from 2016 to 2021. Research limitations/implications The two proposed models can be used to forecast the trend of the system and are grown as an effective extension and supplement of the traditional multivariable grey forecasting models. Practical implications The forecast and analysis of the development prospects of high-tech industries would be useful for the government departments of Guangdong Province and professional forecasters to grasp the future of high-tech industries and formulate decision planning. Originality/value A new multivariable grey prediction model based on fractional order accumulation and its optimized model obtained by reconstructing the background value, which can improve the modelling accuracy of the traditional model, is proposed in this paper.

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“…DGM (1,1), the discrete grey model with a first-order differential equation and one variable, has been shown to be equivalent to the GM(1,1) model under given conditions and to be simpler to use [37]. Xie and Liu discussed in detail the basic principles of DGM(1,1) [38], which has been widely used recently [32,[39][40][41]. Here, we give a concise basic process of DGM(1,1).…”

Section: Fundamental Theoriesmentioning

confidence: 99%

Grey Coupled Prediction Model for Traffic Flow with Panel Data Characteristics

Yang

Xiao

Mao

et al. 2016

Entropy

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This paper studies the grey coupled prediction problem of traffic data with panel data characteristics. Traffic flow data collected continuously at the same site typically has panel data characteristics. The longitudinal data (daily flow) is time-series data, which show an obvious intra-day trend and can be predicted using the autoregressive integrated moving average (ARIMA) model. The cross-sectional data is composed of observations at the same time intervals on different days and shows weekly seasonality and limited data characteristics; this data can be predicted using the rolling seasonal grey model (RSDGM (1,1)). The length of the rolling sequence is determined using matrix perturbation analysis. Then, a coupled model is established based on the ARIMA and RSDGM(1,1) models; the coupled prediction is achieved at the intersection of the time-series data and cross-sectional data, and the weights are determined using grey relational analysis. Finally, numerical experiments on 16 groups of cross-sectional data show that the RSDGM(1,1) model has good adaptability and stability and can effectively predict changes in traffic flow. The performance of the coupled model is also better than that of the benchmark model, the coupled model with equal weights and the Bayesian combination model.

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Fractional-Order Grey Prediction Method for Non-Equidistant Sequences

Cited by 11 publications

References 18 publications

An optimized continuous fractional grey model for forecasting of the time dependent real world cases

An optimized continuous fractional grey model for forecasting of the time dependent real world cases

Analysing the high-tech industry with a multivariable grey forecasting model based on fractional order accumulation

Grey Coupled Prediction Model for Traffic Flow with Panel Data Characteristics

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