Fractional‐Order Accumulative Linear Time‐Varying Parameters Discrete Grey Forecasting Model

Gao, Pumei; Zhan, Jun; Liu, Jiefang

doi:10.1155/2019/6343298

Cited by 6 publications

(5 citation statements)

References 29 publications

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“…In addition to the model proposed in this paper, the models used for the comparative analysis also include other nine diferent types of discrete grey models with hyperparameters, which are LSSVR [32], CFDGM (1, 1) [33], FDGM (1, 1) [34], FNDGM (1, 1, k, c) [35], FDGMP (1, 1, N) [36], FDGM (1, 1, t α ) [37], FGDGMP (1, 1, N, α) [38], WDGM (1, 1) [39], and the FTDGM (1, 1) model [40]. Te reasons why these models are selected for comparative analysis are that they all belong to excellent prediction models and all contain hyperparameters, which make them have strong competitive ability.…”

Section: Data Collectionmentioning

confidence: 99%

A New Conformable Fractional-Order Time-Delay Grey Bernoulli Model with the Arithmetic Optimization Algorithm and Its Application in Rural Regional Economy

Wang

Liu

Yang

et al. 2023

Journal of Mathematics

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To further promote the development of the grey system theory, this paper develops a novel conformable fractional-order grey Bernoulli model with a time-delay effect, namely, the CFTDNGBM (1, 1) model. In addition, the arithmetic optimization algorithm (AOA) is incorporated into the system of the model to solve the hyperparameters existing in the model. Compared with the previous grey prediction models, the CFTDNGBM (1, 1) model with a conformable fractional-order accumulation operation (CFAO), time-delay factor, and Bernoulli parameter has stronger compatibility in structure. The proposed model and its nine competitive models with excellent performance are used to predict and analyze the consumption level and per capita consumption expenditure of rural residents in China to verify the feasibility of the proposed method. The case results show that in both cases, the seven descriptive indicators of the CFTDNGBM (1, 1) model are higher than those of its competing models. Therefore, the CFTDNGBM (1, 1) model has a certain application value.

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Section: Data Collectionmentioning

confidence: 99%

A New Conformable Fractional-Order Time-Delay Grey Bernoulli Model with the Arithmetic Optimization Algorithm and Its Application in Rural Regional Economy

Wang

Liu

Yang

et al. 2023

Journal of Mathematics

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“…Grey fractional DGM(1,1) model Meng and Zeng (2016), Wu et al (2014b) Grey fractional NDGM(1,1) model Li et al (2021), Liu and Wu, (2021), Wu et al (2014a) Grey fractional discrete grey power model Yang and Zhao (2015) Grey fractional TDGM(1,1) model Gao et al (2019) Grey DNDGM(2,1) model…”

Section: Classification Of Grey Forecasting Modelsmentioning

confidence: 99%

A summary of grey forecasting models

Xie

2022

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PurposeThe purpose of this paper is to summarize progress of grey forecasting modelling, explain mechanism of grey forecasting modelling and classify exist grey forecasting models.Design/methodology/approachGeneral modelling process and mechanism of grey forecasting modelling is summarized and classification of grey forecasting models is done according to their differential equation structure. Grey forecasting models with linear structure are divided into continuous single variable grey forecasting models, discrete single variable grey forecasting models, continuous multiple variable grey forecasting models and discrete multiple variable grey forecasting models. The mechanism and traceability of these models are discussed. In addition, grey forecasting models with nonlinear structure, grey forecasting models with grey number sequences and grey forecasting models with multi-input and multi-output variables are further discussed.FindingsIt is clearly to explain differences between grey forecasting models with other forecasting models. Accumulation generation operation is the main difference between grey forecasting models and other models, and it is helpful to mining system developing law with limited data. A great majority of grey forecasting models are linear structure while grey forecasting models with nonlinear structure should be further studied.Practical implicationsMechanism and classification of grey forecasting models are very helpful to combine with suitable real applications.Originality/valueThe main contributions of this paper are to classify models according to models' structure are linear or nonlinear, to analyse relationships and differences of models in same class and to deconstruct mechanism of grey forecasting models.

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“…Definition 4 (see [23]). Assume the nonnegative sequence X (0) , X (r) is defined as Definition 3. e equation…”

Section: Definition 3 (Seementioning

confidence: 99%

Energy Consumption Predication in China Based on the Modified Fractional Grey Prediction Model

Liu

Gao²

2021

Journal of Mathematics

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China’s increasing energy consumption poses challenges to economy and environment. How to predict the energy consumption accurately and regulate the future energy consumption production is a problem worth studying. In this paper, the fractional order cumulative linear time-varying parameter discrete grey prediction model (FTDGM (1, 1) model) is introduced. Firstly, the data are preprocessed by buffer operators, and then, the FTDGM (1, 1) model is established. In this paper, the parameter estimation method and the specific process of model establishment are presented. Finally, the models of energy consumption in China are built. The advantages and prediction accuracy of the model established in this paper are analyzed, and the data in the following years are effectively predicted, so as to provide theoretical support for the government to formulate reasonable energy policies.

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Fractional‐Order Accumulative Linear Time‐Varying Parameters Discrete Grey Forecasting Model

Cited by 6 publications

References 29 publications

A New Conformable Fractional-Order Time-Delay Grey Bernoulli Model with the Arithmetic Optimization Algorithm and Its Application in Rural Regional Economy

A New Conformable Fractional-Order Time-Delay Grey Bernoulli Model with the Arithmetic Optimization Algorithm and Its Application in Rural Regional Economy

A summary of grey forecasting models

Energy Consumption Predication in China Based on the Modified Fractional Grey Prediction Model

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