Improved grey prediction model based on exponential grey action quantity

doi:10.21629/JSEE.2018.03.13

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (3): 560-570.doi: 10.21629/JSEE.2018.03.13

• Systems Engineering • Previous Articles Next Articles

Improved grey prediction model based on exponential grey action quantity

Kedong YIN^1,²(), Yan GENG¹(), Xuemei LI^1,^2,*()

¹ School of Economics, Ocean University of China, Qingdao 266100, China
² Marine Development Studies Institute, Ocean University of China, Qingdao 266100, China

Received:2017-04-06 Online:2018-06-28 Published:2018-07-02
Contact: Xuemei LI E-mail:yinkedong@126.com;gengyan758@126.com;lixuemei@ouc.edu.cn
About author:YIN Kedong was born in 1965. He received his B.E. degree from Nanjing University of Science and Technology in 1988 and M.Ec. degree from Ocean University of China. He is currently a professor, and a D.B.A. supervisor at Ocean University of China. His research interests include quantitative economic analysis and modeling, risk management and control, marine disaster assessment, marine resources and environmental management. E-mail: yinkedong@126.com|GENG Yan was born in 1993. He received his B.S. degree from Ocean University of China in 2015. He is currently working toward his M.Ec. degree at Ocean University of China. His research interests include quantitative economic analysis and modeling, system optimization and risk management and control. E-mail: gengyan758@126.com|LI Xuemei was born in 1985. She received her B.S., M.S., and Ph.D. degrees in mathematics and applied mathematics, system engineering, and management science and engineering from Yantai University, Nanjing University of Aeronautics and Astronautics. She has visited University of Waterloo, Canada as a visiting scholar. She is a lecturer of Ocean University of China now. She has published 30 research papers. Her research interests include grey systems and marine economy. E-mail: lixuemei@ouc.edu.cn
Supported by:
the National Key Research and Development Program of China(2016YFC1402000);the National Science Foundation of China(41701593);the National Science Foundation of China(71371098);the National Science Foundation of China(71571157);the National Social Science Fund Major Project(14ZDB151);The work was supported by the National Key Research and Development Program of China (2016YFC1402000), the National Science Foundation of China (41701593; 71371098; 71571157), and the National Social Science Fund Major Project (14ZDB151)

Abstract

Abstract:

With the passage of time, it has become important to investigate new methods for updating data to better fit the trends of the grey prediction model. The traditional GM(1,1) usually sets the grey action quantity as a constant. Therefore, it cannot effectively fit the dynamic characteristics of the sequence, which results in the grey model having a low precision. The linear grey action quantity model cannot represent the index change law. This paper presents a grey action quantity model, the exponential optimization grey model (EOGM(1,1)), based on the exponential type of grey action quantity; it is constructed based on the exponential characteristics of the grey prediction model. The model can fully reflect the exponential characteristics of the simulation series with time. The exponential sequence has a higher fitting accuracy. The optimized result is verified using a numerical example for the fluctuating sequence and a case study for the index of the tertiary industry’s GDP. The results show that the model improves the precision of the grey forecasting model and reduces the prediction error.

Key words: exponential of grey action quantity, optimal algorithm, grey forecasting, mathematical modeling

Kedong YIN, Yan GENG, Xuemei LI. Improved grey prediction model based on exponential grey action quantity[J]. Journal of Systems Engineering and Electronics, 2018, 29(3): 560-570.

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References 38

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Sequence	$-a$	GM(1, 1)/%	LGM(1, 1)/%	EOGM(1, 1)/%
$X_1^{(0)} $	0.1	0.105 2	0.119 6	0.115 1
$X_2^{(0)} $	0.2	0.498 3	0.493 2	0.362 1
$X_3^{(0)} $	0.4	2.613 4	2.614 0	0.810 0
$X_4^{(0)} $	0.6	8.182 8	5.493 9	1.364 8
$X_5^{(0)} $	1.0	23.543 7	23.547 2	1.955 1

Sequence	$-a$	GM(1, 1)/%	LGM(1, 1)/%	EOGM(1, 1)/%
$X_1^{(0)} $	0.5	8.836 9	8.484 1	14.293 9
$X_2^{(0)} $	1	7.563 9	8.575 2	5.268 9
$X_3^{(0)} $	2	8.556 0	8.389 8	10.630 7
$X_4^{(0)} $	4	10.028 0	15.588 4	13.116 6
$X_5^{(0)} $	10	9.926 4	9.762 2	15.952 5

Sequence	$-a$	GM(1, 1)/%	LGM(1, 1)/%	EOGM(1, 1)/%
$M_1^{(0)} $	0.1	4.297 6	5.521 5	3.469 3
$M_2^{(0)} $	0.2	10.579 8	13.102 6	7.394 1
$M_3^{(0)} $	0.4	3.952 7	7.874 9	2.378 6
$M_4^{(0)} $	0.6	14.498 3	13.610 8	9.959 2
$M_5^{(0)} $	1.0	29.909 4	34.977 6	4.320 1

Number	Actual value	GM(1, 1) predictive value	LGM(1, 1) predictive value	EOGM(1, 1) predictive value	GM(1, 1) -RPE/%	LGM(1, 1) -RPE/%	EOGM(1, 1) -RPE/%
1	100	100	100	100	0	0	0
2	97.024 9	97.067 2	97.264 9	97.016 7	0.043 6	0.247 4	0.008 5
3	95.084 1	95.090 4	95.320 5	95.079 6	0.006 6	0.248 6	0.004 7
4	93.172 4	93.153 9	93.405 2	93.166 8	0.019 9	0.249 9	0.006 0
5	91.289 3	91.256 8	91.518 7	91.284 0	0.035 6	0.251 3	0.005 8
6	89.434 5	89.398 4	89.660 5	89.430 1	0.040 4	0.252 7	0.004 9
7	87.607 5	87.577 8	87.830 2	87.601 9	0.033 9	0.254 2	0.006 4
8	85.808 1	85.794 3	86.027 4	85.802 9	0.016 1	0.255 6	0.006 1

Number	Actual value	GM(1, 1) predictive value	LGM(1, 1) predictive value	EOGM(1, 1) predictive value	GM(1, 1) -RPE/%	LGM(1, 1) -RPE/%	EOGM(1, 1) -RPE/%
9	84.026 9	84.047 1	84.251 6	84.025 8	0.024 0	0.267 4	0.001 3
10	82.282 5	82.335 5	82.502 5	82.280 5	0.064 4	0.267 4	0.002 4

Improved grey prediction model based on exponential grey action quantity

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Year	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014
Index	1 590.7	1 815.3	2 106.8	2 327.1	2 547.1	2 794.1	3 059.7	3 303.3	3 576.0	3 856.6

Year	Actualvalue	GM(1, 1)predictive value	LGM(1, 1)predictive value	EOGM(1, 1)predictive value	GM(1, 1)-RPE/%	LGM(1, 1)-RPE/%	EOGM(1, 1)-RPE/%
2005	1 590.7	1 590.7	1 590.7	1 590.7	0	0	0
2006	1 815.3	1 896.7	1 717.4	1 847.3	4.451 1	5.393 0	1.762 8
2007	2 106.7	2 084.3	1 958.7	2 077.8	1.063 3	7.025 2	1.371 8
2008	2 327.1	2 291.1	2 201.0	2 302.6	1.547 0	5.418 8	1.052 8
2009	2 547.4	2 518.5	2 444.2	2 536.2	1.134 5	4.051 2	0.439 7
2010	2 794.1	2 768.5	2 688.3	2 786.9	0.916 2	3.786 6	0.257 7
2011	3 059.7	3 043.2	2 933.5	3 056.4	0.539 3	4.124 6	0.107 9
2012	3 303.3	3 345.3	3 179.6	3 333.8	1.271 5	3.744 7	0.923 3

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