纵横维度视角下的新型季节离散灰色预测模型及其应用

doi:10.16381/j.cnki.issn1003-207x.2022.2444

Abstract

Abstract:

Seasonal data have multiple complex characteristics such as seasonal fluctuation， cycle coherence， and stage variability， which bring challenges to the scientific construction of its forecasting models. To this end， firstly based on the matrixed processing method of time-series data， the dual perspectives of transverse and longitudinal dimensions of seasonal volatility characteristics are considered. Then， a new real domain fractional discrete grey prediction model is constructed through the introduction of dummy variables and the differential design of accumulation orders， realizing the effective simulation of the characteristics of seasonal data cycle coherence and stage variability. And a particle swarm algorithm is used to synchronize and optimize each variable of the new model in the real domain to further improve the modeling performance of the new model. Also， the modeling by two literature cases shows that the new model error decreases by about 77% and 82%， respectively， compared with the comparative literature models. Finally， the new model is applied to solve the forecasting problem of China's quarterly GDP data， and the results show that the error of the new model is 0.813%， while others are 2.545%， 1.517% and 2.667%， respectively. The research results provide a new modeling tool for studying the forecasting problem of seasonal data， which is of positive significance for improving and enriching the grey forecasting model method system.

Key words: seasonal discrete grey forecasting model, real domain differentiation fractional order, dual perspective of transverse and longitudinal dimensions, quarterly GDP forecasting

CLC Number:

N941.5

Xiaoyi Gou, Chuanmin Mi, Bo Zeng, Mingzhu Li, Yingting Xu. A Novel Seasonal Discrete Grey Forecasting Model based on Transverse and Longitudinal Dimensions and Its Application[J]. Chinese Journal of Management Science, 2025, 33(7): 178-186.

Figures/Tables 9

参数	FDGM_SD∙PSO	SGM(1,1)	APL-SFGM(1,1)	PSO-GM(1,1)	GM(1,1)
$Δ ¯ s$	0.97	2.90	2.97	17.81	17.86
$Δ ¯ p$	0.61	6.13	17.34	23.97	24.21
$Δ ¯$	0.87	3.82	7.08	19.57	19.67

参数	FDGM_SD∙PSO	FMGM(1,‍N)	NSGM(1,N)	GM(1,1)	ARIMA	SVM	LSTM
$Δ ¯ s$	0.7734	4.3618	6.9542	7.4766	4.3606	11.0487	8.6623
$Δ ¯ p$	0.8013	3.6198	8.0850	8.8688	7.4493	23.9512	11.3460
$Δ ¯$	0.7814	4.2546	7.1176	7.6779	5.9050	12.8919	9.0598

参数	参数值	参数	参数值	参数	参数值	参数	参数值
r₁	-0.429	$μ 11$	0.281	$μ 21$	0.018	$μ 31$	45453.493
r₂	-0.823	$μ 12$	0.030	$μ 22$	0.531	$μ 32$	-11364.424
r₃	-0.622	$μ 13$	0.072	$μ 23$	0.951	$μ 33$	23343.417
r₄	0.815	$μ 14$	1.060	$μ 24$	0.792	$μ 34$	83606.316

时间	原始数据	FDGM_SD∙PSO		FMGM(1,N)		PSO-FDGGM(1,1)		SGM(1,1)
时间	原始数据	建模结果	误差	建模结果	误差	建模结果	误差	建模结果	误差
模拟检验
2013Q1	129449.6	129449.600	0.000	129449.600	0.000	129449.600	0.000	129449.600	0.000
2013Q2	143518.7	143518.700	0.000	140382.161	2.185	143518.700	0.000	141198.563	1.617
2013Q3	152222.7	152222.700	0.000	152713.449	0.322	152222.700	0.000	151547.298	0.444
2013Q4	167772.3	167772.300	0.000	167254.883	0.308	167772.300	0.000	170553.853	1.658
2014Q1	140759.8	140380.382	0.270	136400.963	3.097	135452.339	3.771	135521.105	3.722
2014Q2	156489.6	156329.309	0.102	148293.426	5.238	152858.166	2.321	153983.285	1.602
2014Q3	165484.7	165396.966	0.053	164523.990	0.581	161841.015	2.202	165269.038	0.130
2014Q4	180828.9	180898.550	0.039	181351.468	0.289	179850.821	0.541	185996.528	2.858
2015Q1	151137.9	151239.244	0.067	151818.037	0.450	150837.844	0.199	147791.765	2.214
2015Q2	168549.7	168706.232	0.093	164523.703	2.389	168214.258	0.199	167925.589	0.370
2015Q3	176597.7	177011.225	0.234	181281.210	2.652	177657.759	0.600	180233.203	2.059
2015Q4	192572.9	193074.298	0.260	198461.244	3.058	196271.572	1.921	202837.448	5.330
2016Q1	162410	165307.444	1.784	169167.680	4.161	167556.879	3.169	161173.464	0.761
2016Q2	181408.2	182129.582	0.398	182037.116	0.347	185371.651	2.185	183130.290	0.949
2016Q3	191010.6	190917.832	0.049	198905.246	4.133	195154.279	2.169	196552.288	2.901
2016Q4	211566.2	210533.468	0.488	216157.800	2.170	214560.029	1.415	221203.218	4.555
2017Q1	181867.7	180721.853	0.630	186908.863	2.772	184340.051	1.359	175766.798	3.355
2017Q2	201950.3	200482.239	0.727	199802.167	1.064	203473.277	0.754	199711.690	1.108
2017Q3	212789.3	212528.294	0.123	216678.511	1.828	213411.818	0.293	214348.972	0.733
2017Q4	235428.7	235819.705	0.166	233927.348	0.638	234193.940	0.524	241231.903	2.465
2018Q1	202035.7	199124.611	1.441	204665.532	1.302	200846.150	0.589	191681.475	5.125
2018Q2	223962.2	221647.823	1.033	217538.880	2.868	222230.567	0.773	217794.440	2.754
2018Q3	234474.3	234474.301	0.000	234389.783	0.036	232118.668	1.005	233757.045	0.306
2018Q4	258808.9	258200.278	0.235	251608.926	2.782	255008.831	1.468	263074.071	1.648
2019Q1	217168.3	218315.070	0.528	222314.118	2.370	216969.663	0.091	209037.136	3.744
2019Q2	241502.6	242007.973	0.209	235151.931	2.630	241523.758	0.009	237514.479	1.651
2019Q3	251046.3	251074.738	0.011	251965.353	0.366	251142.540	0.038	254922.407	1.544
2019Q4	276798	277981.091	0.427	269145.542	2.765	276953.269	0.056	286893.922	3.647
预测检验
2020Q1	205244.8	236581.148	15.268	239810.692	16.841	232682.674	13.368	227964.252	11.069
2020Q2	248347.7	248347.700	0.000	252607.678	1.715	261298.514	5.215	259020.056	4.297
2020Q3	264355.7	257284.107	2.675	269379.737	1.900	270420.233	2.294	278004.172	5.163
2020Q4	295618.8	295618.800	0.000	286518.228	3.078	300022.831	1.490	312870.524	5.836
2021Q1	247985	247760.060	0.091	257141.506	3.692	247986.274	0.001	248605.110	0.250
2021Q2	281528	278354.425	1.127	269896.582	4.132	281530.285	0.001	282472.839	0.336
2021Q3	289919.3	290125.537	0.071	286626.797	1.136	289919.709	0.001	303175.858	4.572
2021Q4	324237.4	326433.425	0.677	303723.600	6.327	324236.572	0.001	341199.159	5.231

参数

FDGM_SD∙PSO

FMGM

(1,N)

PSO-FDGGM

(1,1)

SGM(1,1)

Δ ¯ s

0.335

1.886

1.152

2.116

Δ ¯ p

2.489

4.853

2.796

4.594

Δ ¯

0.813

2.545

1.517

2.667

References 31

[1]	龙会典，严广乐.基于SARIMA、GM（1，1）和BP神经网络集成模型的GDP时间序列预测研究［J］.数理统计与管理，2013，32（5）：814-822.
	Long H D， Yan G L. Research on GDP time series forecasting based on integrating SARIMA， GM（1，1） and BP neural networks［J］. Journal of Applied Statistics and Management，2013，32（5）：814-822.
[2]	蒋锋，张文雅.机器学习方法在经济研究中的应用［J］.统计与决策，2022，38（4）：43-49.
	Jiang F， Zhang W Y. Application of machine learning methods in economic research［J］. Statistics & Decision，2022，38（4）：43-49.
[3]	Jiang Y， Guo Y J， Zhang Y H. Forecasting China's GDP growth using dynamic factors and mixed-frequency data［J］. Economic Modelling， 2017， 66：132-138.
[4]	曾波，李惠，余乐安，等.季节波动数据特征提取与分数阶灰色预测建模［J］.系统工程理论与实践，2022，42（2）：471-486.
	Zeng B， Li H， Yu L A， et al. Feature extraction and fractional grey prediction modeling of seasonal fluctuation data［J］. Systems Engineering-Theory & Practice， 2022，42（2）：471-486.
[5]	Liu S F， Yang Y J， Forrest J. Grey data analysis： Methods，models and applications［M］.London： Springer， 2016.
[6]	Xin X， Hu X， Guo H. A hybrid optimized grey seasonal variation index model improved by whale optimization algorithm for forecasting the residential electricity consumption［J］. Energy， 2021， 234： 121127.
[7]	Zhou W J， Tao H H， Ding S， et al. Electricity consumption and production forecasting considering seasonal patterns： An investigation based on a novel seasonal discrete grey model［J］. Journal of the Operational Research Society， 2023， 74（5）： 1346-1361.
[8]	Zhou W J， Wu X L， Ding S， et al. Predictive analysis of the air quality indicators in the yangtze river delta in china： An application of a novel seasonal grey model ［J］.Science of the Total Environment， 2020， 748： 141428.
[9]	Zhou W J， Wu X L， Ding S， et al. Predictions and mitigation strategies of PM_2.5 concentration in the Yangtze River Delta of China based on a novel nonlinear seasonal grey model［J］.Environmental Pollution，2021，276： 116614.
[10]	张国政，罗党.基于季节波动序列的灰色预测模型及其应用［J］.统计与决策，2021，37（23）：23-27.
	Zhang G Z， Luo D. Grey forecasting model based on seasonal fluctuation sequence and its application［J］. Statistics & Decision，2021，37（23）：23-27.
[11]	Wang Z X， Li Q， Pei L L. A seasonal GM（1，1） model for forecasting the electricity consumption of the primary economic sectors［J］.Energy，2018，154： 522-534.
[12]	Wang Z X， Wang Z W， Li Q. Forecasting the industrial solar energy consumption using a novel seasonal GM（1，1） model with dynamic seasonal adjustment factors［J］. Energy， 2020， 200： 117460.
[13]	Li N， Wang J L， Wu L F， et al. Predicting monthly natural gas production in China using a novel grey seasonal model with particle swarm optimization［J］. Energy， 2021， 215： 119118.
[14]	Du P， Guo J， Sun S L， et al. A novel two-stage seasonal grey model for residential electricity consumption forecasting ［J］. Energy， 2022， 258： 124664.
[15]	Wang Z X， He L Y， Zhao Y F. Forecasting the seasonal natural gas consumption in the US using a gray model with dummy variables［J］. Applied Soft Computing， 2021， 113： 108002.
[16]	Zhou W J， Ding S. A novel discrete grey seasonal model and its applications［J］. Communications in Nonlinear Science and Numerical Simulation， 2021， 93： 105493.
[17]	Zhou W J， Jiang R R， Ding S， et al A novel grey prediction model for seasonal time series［J］. Knowledge-Based Systems， 2021， 229： 107363.
[18]	王正新，赵宇峰.含季节性虚拟变量的GM（1，1）模型及其应用［J］.系统工程理论与实践，2020，40（11）：2981-2990.
	Wang Z X， Zhao Y F. GM（1，1） model with seasonal dummy variables and its application［J］.Systems Engineering-Theory & Practice，2020，40（11）：2981-2990.
[19]	Wang Z X， Li Q， Pei L L. Grey forecasting method of quarterly hydropower production in China based on a data grouping approach［J］. Applied Mathematical Modelling， 2017， 51： 302-316.
[20]	Chen H B， Pei L L， Zhao Y F. Forecasting seasonal variations in electricity consumption and electricity usage efficiency of industrial sectors using a grey modeling approach［J］. Energy， 2021， 222： 119952.
[21]	Li X M， Guo X C， Liu L N， et al. A novel seasonal grey model for forecasting the quarterly natural gas production in China ［J］. Energy Reports， 2022（8）：9142-9157.
[22]	Ding S， Tao Z， Li R J， et al. A novel seasonal adaptive grey model with the data-restacking technique for monthly renewable energy consumption forecasting ［J］. Expert Systems with Applications， 2022， 208： 118115.
[23]	Qian W Y， Wang J. An improved seasonal GM（1，1） model based on the HP filter for forecasting wind power generation in China［J］. Energy， 2020， 209： 118499.
[24]	Xia M， Wong W K. A seasonal discrete grey forecasting model for fashion retailing［J］. Knowledge-Based Systems， 2014， 57： 119-126.
[25]	Xiao X P， Yang J W， Mao S H， et al. An improved seasonal rolling grey forecasting model using a cycle truncation accumulated generating operation for traffic flow［J］. Applied Mathematical Modelling， 2017， 51： 386-404.
[26]	Tang T， Jiang W H， Zhang H， et al. GM（1，1） based improved seasonal index model for monthly electricity consumption forecasting［J］.Energy，2022，252： 124041.
[27]	Zhou W J， Pan J， Tao H H， et al. A novel grey seasonal model based on cycle accumulation generation for forecasting energy consumption in China［J］. Computers & Industrial Engineering， 2022， 163： 107725.
[28]	Wang X L， Xie N M， Yang L. A flexible grey Fourier model based on integral matching for forecasting seasonal PM_2.5 time series［J］. Chaos， Solitons & Fractals， 2022， 162： 112417.
[29]	周坤，高晓辉，李廉水.基于EMD-XGB-ELM和FSGM双元处理的碳排放交易价格集成预测［J］.中国管理科学，2024， 32（10）： 325-334.
	Zhou K， Gao X H， Li L S. Integrated carbon emission trading price prediction based on EMD -XGB-Elm and FSGM form the perspective of dual processing［J］. Chinese Journal of Management Science，2024，32（10）： 325-334.
[30]	曾波，余乐安，刘思峰，等.灰色累加算子与灰色累减算子的统一及其应用［J］.系统工程理论与实践，2021，41（10）：2710-2720.
	Zeng B， Yu L A， Liu S F， et al. Unification of grey accumulation operator and the inverse operator and its application［J］. Systems Engineering-Theory &Practice，2021，41（10）： 2710-2720.
[31]	曾波，李树良，孟伟. 灰色预测理论及其应用［M］. 北京：科学出版社， 2020.
	Zeng B， Li S L， Meng W. Grey prediction theory and its applications ［M］. Beijing： Science Press，2020.

季度	2022年	2023年	2024年	2025年
第一季度	271274.995	277406.817	290933.520	307371.132
第二季度	309615.296	255674.031	266116.277	284258.743
第三季度	315214.918	296381.203	303183.373	315904.219
第四季度	354696.513	384081.425	415531.130	449242.091

A Novel Seasonal Discrete Grey Forecasting Model based on Transverse and Longitudinal Dimensions and Its Application

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 9

References 31

Related Articles 15

Metrics

Comments

Recommended 0

[1]	Yunjie Mei,Xiangyan Zeng,Shuli Yan. A Matrix Autoregressive Time-delay Grey Multivariable Model for Three-parameter Interval Grey Number Sequences [J]. Chinese Journal of Management Science, 2024, 32(9): 48-58.
[2]	Shuliang Li,Shuangyi Yang,Bo Zeng,Wei Meng,Yun Bai. Unbiased and Adaptive of Discrete Grey Prediction Model and Its Application [J]. Chinese Journal of Management Science, 2024, 32(8): 149-158.
[3]	Lianyi Liu,Sifeng Liu,Lifeng Wu. New Energy Vehicle Sales Forecast Based on Siscrete Time Grey Power Model [J]. Chinese Journal of Management Science, 2024, 32(1): 106-114.
[4]	ZHOU Wei-jie, JIANG Hui-min, CHENG Yu-ke, DANG Yao-guo, DING Song. Forecasting Chinese Hydropower Consumption Forecasting by Using the Repeatability Fractional Grey Time Power Model [J]. Chinese Journal of Management Science, 2023, 31(5): 279-286.
[5]	ZENG Bo, GOU Xiao-yi, ZHANG Zhi-wei. Research on the Non-Uniqueness of Solutions of the Mean Difference GM(1,1) Model Based on Interval Grey Interaction [J]. Chinese Journal of Management Science, 2022, 30(10): 247-255.
[6]	XIONG Ping-ping, CHEN Shi-ting, ZHOU Yi-fan, LIU Yu-chun, DING Song. MGM (1, m, N) Model Based on the New Kernel and Degree of Greyness Sequences and Its Application [J]. Chinese Journal of Management Science, 2022, 30(7): 130-139.
[7]	LI Hui, ZENG Bo, ZHOU Wen-hao. Forecasting Domestic Waste Clearing and Transporting Volume by Employing A New Grey Parameter Combination Optimization Model [J]. Chinese Journal of Management Science, 2022, 30(4): 96-107.
[8]	LI Ye, DING Yuan-ping. Construction of Linear Time-varying Parameters DLDGM(1,N) Model Based on Driving Factors Control [J]. Chinese Journal of Management Science, 2022, 30(3): 221-229.
[9]	DUAN Hui-ming, XIAO Xin-ping. Research on Grey Inertial Model and Its Application Property [J]. Chinese Journal of Management Science, 2022, 30(3): 269-279.
[10]	XIA Jie, MA Xin, WU Wen-qing. The Improved FAGM(1, 1) Model Based on Simpson Formula and Its Applications [J]. Chinese Journal of Management Science, 2021, 29(5): 240-248.
[11]	QIAN Li-li, LIU Si-feng, DENG Gui-feng. Grey Off-target Deviation Degree Method for Group Decision-making with Regret Aversion [J]. Chinese Journal of Management Science, 2020, 28(6): 193-200.
[12]	ZENG Bo, LIU Si-feng, BAI Yun, ZHOU Meng. Grey System Modeling Technology for Early Prediction and Warning of Human Diseases [J]. Chinese Journal of Management Science, 2020, 28(1): 144-152.
[13]	DING Song, LI Ruo-jin, DANG Yao-guo. Construction and Application of GM(1,1) Power Model based on the Optimized Initial Condition [J]. Chinese Journal of Management Science, 2020, 28(1): 153-161.
[14]	WU Li-feng, YU Liang, WEN Zhao-xia. GM(0,N) Model for Its Application on Forecasting the Development Cost of Complicated Equipment [J]. Chinese Journal of Management Science, 2019, 27(7): 203-207.
[15]	ZHOU Wei-jie, ZHANG Hong-ru, DANG Yao-guo, WANG Zheng-xin. New Information Priority Accumulated Grey Discrete Model and Its Application [J]. Chinese Journal of Management Science, 2017, 25(8): 140-148.