Discrete grey model with the weighted accumulation. (English) Zbl 1436.62451
Summary: To add greater weight to new information, discrete grey model with the weighted accumulation (WDGM(1,1)) is put forward. This paper proved the stability of WDGM(1,1) disturbance boundary and the influence of the analysis parameter \(\lambda\) on the reduction error. The prediction ability of the WDGM(1,1) is verified by five cases. The results show that WDGM(1,1) not only satisfies the new information priority to a certain extent, but also has better stability. Moreover, the parameter \(\lambda\) in WDGM(1,1) can effectively reduce the reduction error, so that it has better prediction accuracy in practical applications. Therefore, the proposal of WDGM(1,1) is not only very theoretical, but also has good practical significance.
MSC:
| 62M20 | Inference from stochastic processes and prediction |
| 93C41 | Control/observation systems with incomplete information |
References:
| [1] | Chen CI, Hsin PH, Wu CS (2010) Forecasting Taiwan’s major stock indices by the Nash nonlinear grey Bernoulli model. Expert Syst Appl 37(12):7557-7562 · doi:10.1016/j.eswa.2010.04.088 |
| [2] | Dang YG, Liu SF, Liu B (2005) The GM models that x(1)(n) be taken as initial value. Chin J Manag Sci 13(1):133-136 |
| [3] | Ding S, Dang YG, Li XM, Wang JJ, Zhao K (2017) Forecasting Chinese CO2 emissions from fuel combustion using a novel grey multivariable model. J Clean Prod 162:1527-1538 · doi:10.1016/j.jclepro.2017.06.167 |
| [4] | Han Z (1995) Application of exponential cumulative generation method and logarithmic cumulative generation method to grey prediction. China J Highw Transp 8(1):52-57 |
| [5] | Hu P (2016) The DGM(1,1) models that x(1)(n) be taken as initial value. Math Pract Theory 46(17):218-222 · Zbl 1374.93204 |
| [6] | Jiguang Sun (1987) Matrix perturbation analysis. Science Press, Beijing · Zbl 0632.15009 |
| [7] | Li C, Xie XP (2017) The DGM(1,1)atan arc-tangent function and its application. Syst Eng Theory Pract 37(12):3227-3234 |
| [8] | Li GD, Yamaguchi D, Nagai M (2007) A GM(1,1)-Markov chain combined model with an application to predict the number of Chinese international airlines. Technol Forecast Soc Chang 74(8):1465-1481 · doi:10.1016/j.techfore.2006.07.010 |
| [9] | Li ML, Wang W, De G, Ji XH, Tan ZF (2018) Forecasting carbon emissions related to energy consumption in Beijing-Tianjin-Hebei region based on grey prediction theory and extreme learning machine optimized by support vector machine algorithm. Energies 11:2475-2489 · doi:10.3390/en11092475 |
| [10] | Li C, Yang YJ, Liu SF (2019a) A new method to mitigate data fluctuations for time series prediction. Appl Math Model 65:390-407 · Zbl 1481.62059 · doi:10.1016/j.apm.2018.08.017 |
| [11] | Li C, Yang YJ, Liu SF (2019b) Comparative analysis of properties of weakening buffer operators in time series prediction models. Commun Nonlinear Sci Numer Simul 68:257-285 · Zbl 1508.62217 · doi:10.1016/j.cnsns.2018.06.029 |
| [12] | Li SY, Yang X, Li RR (2019c) Forecasting coal consumption in India by 2030:using linear modified linear (MGM-ARIMA) and linear modified nonlinear (BP-ARIMA) combined models. Sustaina bility 11:695-713 · doi:10.3390/su11030695 |
| [13] | Lin YH, Chiu CC, Lee PC, Lin YJ (2012) Applying fuzzy grey modification model on inflow forecasting. Eng Appl Artif Intell 25(4):734-743 · doi:10.1016/j.engappai.2012.01.001 |
| [14] | Liu JF, Liu SF, Fang ZG (2016) A class of new weakening buffer operators whose adjustable intensity can be changed and their applications. Chin J Manag Sci 24(8):172-176 |
| [15] | Lu JS, Xie WD, Zhou HB, Zhang AJ (2016) An optimized nonlinear grey Bernoulli model and its applications. Neurocomputing 177:206-214 · doi:10.1016/j.neucom.2015.11.032 |
| [16] | Ma YS, Dai YZ (1993) Improvement of data generation method in grey system. Syst Sci Compr Stud Agric 9(2):113-116 |
| [17] | Ou SL (2012) Forecasting agricultural output with an improved grey forecasting model based on the genetic algorithm. Comput Electron Agric 85:33-39 · doi:10.1016/j.compag.2012.03.007 |
| [18] | Qian WY, Dang YG, Wang YM (2009) GM(1, 1) model based on weighting accumulated generating operation and its application. Math Pract Theory 39(15):47-51 |
| [19] | Song T (2004) The accumulated generating space. J Shandong Inst Archit Eng 19(1):88-90 |
| [20] | Song ZM, Deng JL (2001) The accumulated generating operation in opposite direction and its use in grey model GOM(1,1). Syst Eng 19(1):66-69 |
| [21] | Song Q, Wang AM (2009) Simulation and prediction of alkalinity in sintering process based on grey least squares support vector machine. J Iron Steel Res 16(5):1-6 · doi:10.1016/S1006-706X(10)60001-5 |
| [22] | Stewart GW (1977) On the perturbation of pseudo-inverses, projections and linear least squares problems. Slam Rev 19(4):634-662 · Zbl 0379.65021 |
| [23] | Sun X, Sun WS, Wang JZ, Zhang YX, Gao YN (2016) Using a grey-Markov model optimized by Cuckoo search algorithm to forecast the annual foreign tourist arrivals to China. Tour Manag 52:369-379 · doi:10.1016/j.tourman.2015.07.005 |
| [24] | Wang YH, Dang YG, Li YQ, Liu SF (2010) An approach to increase prediction precision of GM(1,1) model based on optimization of the initial condition. Expert Syst Appl 37(8):5640-5644 · doi:10.1016/j.eswa.2010.02.048 |
| [25] | Wang QR, Liu L, Wang S, Wang JZ, Liu M (2017) Predicting Beijing’s tertiary industry with an improved grey model. Appl Soft Comput 57:482-494 · doi:10.1016/j.asoc.2017.04.022 |
| [26] | Wu LF, Liu SF, Cui W, Liu DL, Yao TX (2014) Non-homogenous discrete grey model with fractional-order accumulation. Neural Comput Appl 25(5):1215-1221 · doi:10.1007/s00521-014-1605-1 |
| [27] | Wu LF, Gao XH, Xiao YL, Yang YJ, Chen XN (2018) Using a novel multi-variable grey model to forecast the electricity consumption of Shandong province in China. Energy 157:327-335 · doi:10.1016/j.energy.2018.05.147 |
| [28] | Xu N, Dang YG (2018) Characteristic adaptive GM(1,1) model and forecasting of Chinese traffic pollution emission. Syst Eng Theory Pract 38(1):187-196 |
| [29] | Yang BH, Zhang ZQ (2003) The grey model has been accumulated generating operation in reciprocal number and its application. Math Pract Theory 33(10):21-26 |
| [30] | Zeng Bo (2017) Forecasting the relation of supply and demand of natural gas in China during 2015-2020 using a novel grey model. J Intell Fuzzy Syst 32(1):141-155 · doi:10.3233/JIFS-151249 |
| [31] | Zeng B, Li C (2016) Forecasting the natural gas demand in China using a self-adapting intelligent grey model. Energy 112:810-825 · doi:10.1016/j.energy.2016.06.090 |
| [32] | Zhao HR, Guo S (2016) An optimized grey model for annual power load forecasting. Energy 107:272-286 · doi:10.1016/j.energy.2016.04.009 |
| [33] | Zhou WJ, Zhang HR, Dang YG, Wang ZX (2017) New information priority accumulated grey discrete model and its application. Chin J Manag Sci 25(8):140-148 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
