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A Novel Fractional-Order Grey Prediction Model and Its Modeling Error Analysis

1,2,*, 1 and 1
1
Chongqing Engineering Technology Research Center for Information Management in Development, Chongqing Technology and Business University, Chongqing 400067, China
2
School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 611731, China
*
Author to whom correspondence should be addressed.
Information 2019, 10(5), 167; https://doi.org/10.3390/info10050167
Received: 23 March 2019 / Revised: 28 April 2019 / Accepted: 28 April 2019 / Published: 5 May 2019
(This article belongs to the Section Information Processes)
PDF [671 KB, uploaded 5 May 2019]

Abstract

Based on the grey prediction model GM(1,1), a novel fractional-order grey prediction model is proposed and its modeling error is systematically studied. In this paper, exponential data sequences are generated for numerical simulation. Via the numerical simulation method, the mean absolute percentage error (MAPE) of the fractional-order GM(1,1) with different values of order and development coefficient is compared to the GM(1,1) and the discrete GM(1,1). The error distribution of the sequences of exponential data is given. The GM(1,1) and the direct modeling GM(1,1) are both special cases of the fractional-order GM(1,1). The conclusion is helpful to further optimize the grey model using fractional-order operators and to expand the applicable bound of GM(1,1).
Keywords: fractional-order operator; grey prediction model; error analysis fractional-order operator; grey prediction model; error analysis
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Meng, W.; Zeng, B.; Li, S. A Novel Fractional-Order Grey Prediction Model and Its Modeling Error Analysis. Information 2019, 10, 167.

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