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Abstract
The direct grey model (DGM(2,1)) is considered for fluctuation characteristics of the sampling data in Grey system theory. However, its applications are quite uncommon in the past literature. The improvement of the precision of the DGM(2,1) is only presented in few previous researches. Moreover, the evaluation of forecasted performance of the DGM(2,1) model and its applications was not conducted in previous studies. As the results, this study aims to evaluate forecasted performance of the DGM(2,1) and its three modified models, including the Markov direct grey model MDGM(2,1), the Fourier direct grey model FDGM(2,1), and the Fourier Markov direct grey model FMDGM(2,1) in order to determine the application of the DGM(2,1) model in practical applications and academic research. The results demonstrate that the DGM(2,1) model has lower precision than its modified models, while the forecasted precision of the FDGM(2,1) is better than that of MDGM(2,1). Additionally, the FMDGM(2,1) model presents the best performance among all of the modified models of DGM(2,1), which can effectively overcome the fluctuating of the data sample and minimize the predicted error of the DGM(2,1) model. The finding indicated that the FMDGM(2,1) model does not only have advantages with regard to the sample size requirement, but can also be flexibly applied to the large fluctuation and random sequences with a high quality of estimation.
Highlights
The Grey prediction is an effective tool for understanding an uncertain environment with limited information [1]
These models consists of the basic model GM(1,1), the GM(2,1), Verhulst and direct grey model DGM(2,1), which are known as the common prediction models in Grey system theory [2]
In the same manner as the FMGM(1,1) model, a combination of the DGM(2,1), the Fourier series and the Markov chain has been developed, and has been successfully applied to forecast trends in Taiwan’s electronic paper industry [14]; the results indicated that the FMDGM(2,1) model gave a better predicted precision than the FMGM(1,1) and the FM-Verhulst models
Summary
The Grey prediction is an effective tool for understanding an uncertain environment with limited information [1]. These models consists of the basic model GM(1,1), the GM(2,1), Verhulst and direct grey model DGM(2,1), which are known as the common prediction models in Grey system theory [2]. Some defects have been found in the performance of the grey forecasting model and can still be improved [3]. Literature in [6] proposed high accuracy for the optimized DGM(2,1) model, which has the white exponential superposition. The improved precision of DGM(2,1) mainly focused on modifying the whitening differential equation or optimizing the parameter of the grey model
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