Abstract
A novel aging fractional accumulation operator is proposed. The aging accumulation operator can dynamically update the accumulation weight of data and flexibly change the forecast trend by adjusting the aging parameter. In addition, a new aging accumulated grey model is obtained by using the aging accumulation operator to improve the traditional grey model. In the analysis of four examples, the existing grey accumulation operator and prediction method are compared. The results show that the proposed aging accumulation operator and aging accumulation grey model have excellent performance.
Highlights
The traditional grey model still has some shortcomings. e improvements in recent years mainly focus on the following four aspects: (1) Optimization of model background value: traditional background values z(1)(k) 0.5(x(1)(k) + x(1)(k + 1)) are suitable for smooth sequences, which can be optimized to adapt to other situations. e model background value is reconstructed by the Simpson formula, and the unbiased GM(SD) (1, 1) model is obtained [8]
(4) Error correction: the prediction accuracy can be further improved by error analysis of prediction results combined with correction technology. e Fourier error correction method is used to improve the existing grey forecasting model [17]. e triangle residual error correction method is used to eliminate the inherent error of the original grey model, and a new grey prediction model with error correction is proposed [18]
Different from the existing grey accumulation operator, this operator determines the accumulation weight of data at different times from back to front. e addition of new data will push the old data to roll back so that the timeliness of data can be updated dynamically with the change of the system. e aging accumulation operator is introduced into the grey model, and a new aging accumulation grey model AGM (1, 1) is obtained
Summary
If |x(c)(i) − x(c)(i)| < ε (1 < i ≤ m), x(0)(i)| < ε ∗ ij 1 |R(j, i)| (1 < i ≤ m), where g(0) g(1) · · · g(i − 1) − 1. An optimization algorithm is introduced to determine the optimal aging parameter, and four examples are used to prove the effectiveness of the proposed AGM (1, 1) model. Erefore, this paper compares AGM (1, 1) with GM (1, 1) models with different sample sizes, and Table 2 shows the comparison results. E results show that with the increase of the number of samples, the special metabolic function of AGM(1, 1) can reduce the interference of old data and improve the prediction performance of the model. In the fitting and testing stage, MAPE, MAE, and RMSE of AGM (1, 1) are the lowest, which shows that the proposed AGM (1, 1) model has excellent performance in dealing with medium and long-term stationary sequences
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