Research on Optimum Weighted Combination GM(1,1) Model with Different Initial Value

Qiu-mei, Chen; Jin, Li

doi:10.1007/978-3-319-22053-6_39

Cited by 4 publications

(6 citation statements)

References 6 publications

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“…In Equation (20), μ is the mean value of the overall forecast error, α is the level of significance, σ is the total variance, and m is the amount of sample. The value of c 2 − c 1 is defined as the width of confidence interval.…”

Section: Resultsmentioning

confidence: 99%

“…[15–17] used a single component of the first‐order accumulated generating operation (1‐AGO) sequence to generate initial conditions, and Wang et al. [18–21] applied the linear combination of multiple components of 1‐AGO sequence to create initial conditions. Moreover, some researchers tried to multiply or add coefficients to specific components to get initial conditions [22, 23].…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, lots of scholars have done many research studies such as initial sequence pre-processing, background value reconstruction, time response function improvement and initial condition optimisation. In the aspect of initial condition optimisation, Li et al [15][16][17] used a single component of the first-order accumulated generating operation (1-AGO) sequence to generate initial conditions, and Wang et al [18][19][20][21] applied the linear combination of multiple components of 1-AGO sequence to create initial conditions. Moreover, some researchers tried to multiply or add coefficients to specific components to get initial conditions [22,23].…”

Section: Introductionmentioning

confidence: 99%

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A new GM (1,1) model suitable for short‐term prediction of satellite clock bias

Tan

et al. 2022

IET Radar Sonar & Navi

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Due to the sensitivity of spaceborne atomic clock to many factors, the variation law of satellite clock bias (SCB) can be regarded as a grey system. The GM (1,1) model is a most classical and basic model of grey system, which has been successfully applied in SCB prediction. Moreover, many improved models have been proposed and widely used in various forecasts since GM (1,1) was generated. However, the prediction performance of these models is not obviously improved compared with the classical models in clock bias prediction. In view of this, a new GM (1,1) model has been come up with in this paper by optimising fitting model and initial condition. The new fitting model is obtained by differentiating time response function of winterisation, and the new initial condition is generated through one or more components of the original clock bias sequence. The authors employ GPS rapid and precise SCB provided by the International GNSS Service (IGS) for prediction experiments. The results show that the new GM (1,1) model is effective and feasible, and its prediction accuracy and stability are enormously better than that of the classical GM (1,1) model, especially for ultra-short-term prediction.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A new GM (1,1) model suitable for short‐term prediction of satellite clock bias

Tan

et al. 2022

IET Radar Sonar & Navi

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“…The most classical prediction model is GM(1,1), where the first "1" represents the first order differential equation and the second "1" represents a variable. The improvement of the GM(1,1) model has never stopped, mainly in the following five aspects: (1) preprocessing of raw data [14,15,16]; (2) improvement of background value [17,18,19]; (3) initial value improvement [20]; (4) parameter improvement of the model [21,22]; (5) combination improvement of the above method [23].…”

Section: Methods Articlementioning

confidence: 99%

A Novel Dynamic Grey Action Quantity GM(1,1,b) Model and Its Application

2019

ARJOM

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The classical GM(1,1) model treats the grey action quantity as an invariant constant, but changes have occurred within the system as time and space change. If the fixed grey action quantity is still used for modeling, the model will have errors. Aiming at this shortcoming, this paper proposes a GM(1,1,b) model in which the grey action quantity can be dynamically changed. Starting from the background value formula, the model solves the grey action quantity at different time points by the development coefficient, and fits the sequence with the DGM(1,1) model, then brings the obtained time response sequence into the classical GM (1, 1) to replaces the grey action quantity constant, so as to establish a GM(1,1,b) model with dynamic change of grey action quantity. Finally, the model is applied to the example of China's rural residents' consumption index. The numerical example shows that the GM(1,1,b) model proposed in this paper effectively improves the prediction accuracy of the model and verifies the effectiveness and practicability of the improved model.

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“…Another study by Wang et al, [13] introduced a new approach for grey model improvement based on a modified initial condition using the first item and the last item of X (1) to enhance prediction accuracy of a traditional GM(1,1) model. Chen and Li [14] also proposed a new technique for a GM(1,1) model using an optimal weighted combination with a different initial value. These improvement the new grey models make to the initial condition may raise the forecast accuracy in certain practical applications.…”

Section: Introductionmentioning

confidence: 99%

An Initial Condition Optimization Approach for Improving the Prediction Precision of a GM(1,1) Model

Madhi

Mohamed

2017

MCA

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Grey model GM(1,1) has attained excellent prediction accuracy with restricted data and has been broadly utilized in a range of areas. However, the GM(1,1) forecasting model sometimes yields large forecasting errors which directlyaffect the simulation and prediction precision directly. Therefore, the improvement of the GM(1,1) model is an essential issue, and the current study aims to enhance the prediction precision of the GM(1,1) model. Specifically, in order to improve the prediction precision of GM(1,1) model, it is necessary to consider improving the initial condition in the response function of the model. Consequently, the purpose of this paper is to put forward a new method to enhance the performance of the GM(1,1) model by optimizing its initial condition. The minimum sum of squared error was used to optimize the new initial condition of the model. The numerical outcomes show that the improved GM(1,1) model provides considerably better performance than traditional grey model GM(1,1) . The result demonstrates that the improved grey model GM(1,1) achieves the objective of minimizing the forecast errors.

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Research on Optimum Weighted Combination GM(1,1) Model with Different Initial Value

Cited by 4 publications

References 6 publications

A new GM (1,1) model suitable for short‐term prediction of satellite clock bias

A new GM (1,1) model suitable for short‐term prediction of satellite clock bias

A Novel Dynamic Grey Action Quantity GM(1,1,b) Model and Its Application

An Initial Condition Optimization Approach for Improving the Prediction Precision of a GM(1,1) Model

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