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Chinese Journal of Management Science ›› 2020, Vol. 28 ›› Issue (1): 153-161.doi: 10.16381/j.cnki.issn1003-207x.2020.01.013

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Construction and Application of GM(1,1) Power Model based on the Optimized Initial Condition

DING Song1,2, LI Ruo-jin1, DANG Yao-guo3   

  1. 1. School of Economics, Zhejiang University of Finance and Economics, Hangzhou 310018, China;
    2. Center for Regional Economy&Integrated Development, Zhejiang University of Finance&Economics, Hangzhou 310018, China;
    3. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
  • Received:2016-12-25 Revised:2019-07-10 Online:2020-01-20 Published:2020-01-19

Abstract: The GM(1,1) power model has been used in many fields, such as electricity loading forecast, industrial waste emissions, and urban water consumption, ever since it was proposed by professor Deng.Specifically, this model has wide applications, because it has a dynamic adaptive power index, which can adapt to different characteristics of various sequences. However, this model still has its drawbacks that the power exponent is difficult to obtain and the conventional initial condition does not satisfy the principle of new information priority. Therefore, large error gap exists between forecasts and original observations. To this end, approaches on collaborative optimization of power exponent and initial condition are put forward to obtain a superior grey power model. The detailed procedures for this novel can be described as follows.
Initially, based on the principle of new information priority, the function of controlling weight is introduced to optimize the initial condition, which reflects the effect of new-old information on the trend of the system together with the max use of existing information and expresses the changing law. Subsequently, the non-linear optimized model is constructed to optimize the power exponent and initial condition together with the target of minimizing the average relative error. Then the optimal initial condition and power index can be obtained. Lastly, this new proposed grey power model is employed to forecast the amount of online shopper, compared with three competing models, namely GPM(1,1,x(1)(1)), GPM(1,1,x(1)(n)), and GPM(1,1,β). Experimental results illustrate that the novel optimized model achieves the best performance among the four models and gets the minimum value of average relative error theoretically. Therefore, this novel grey model can be used for future amount prediction of China's online shopper.
For the future forecasts, the novel grey power model having optimized initial condition and optimal power exponent is utilized to estimate the amount of China's online shopper from 2016 to 2020. Additionally, the real observations from 2016 to 2018 are collected to match the forecasted values. The compared results show that the errors between forecasts and original data from 2016 to 2018 are all less than 10%, which means the great performance of this proposed model. Therefore, conclusions can be made that this newly designed grey power model has good validity and practicability and it can be further used in other fields.Moreover, according to the predicted results, the amount of China's online shoppers will reach 900 million in 2020. Many residents will shop on the internet instead of outdoor shopping.

Key words: grey prediction, GM(1,1) power model, optimizing the initial condition, online shopper

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