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

摘要/Abstract

摘要：

季节数据具有季节波动性、周期连贯性、阶段差异性等多重复杂特征，这为其预测模型的科学构建带来了挑战。为此，本文首先基于时序数据矩阵化处理方法，实现了纵横维度双重视角的季节波动性特征考虑；其次，通过虚拟变量的引入及累加阶数的差异化设计，构建了新型实域分数阶离散灰色预测模型，实现了季节数据周期连贯性与阶段差异性等特征的有效模拟；然后，利用粒子群算法对新模型各变量阶数在实域范围内进行同步优化，以进一步提高新模型建模性能，通过两篇文献案例建模显示，新模型误差较对比文献模型分别下降约77%与82%。最后，将新模型用于解决我国GDP季度数据的预测问题，结果显示，新模型误差为0.813%，其他同类模型误差分别为2.545%、1.517%与2.667%。本研究成果为研究季节数据的预测问题提供了一种新的建模手段，对完善和丰富灰色预测模型方法体系具有积极意义。

关键词: 季节离散灰色预测模型, 实域差异化分数阶, 纵横维度双重视角, 季度GDP预测

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

中图分类号:

N941.5

苟小义, 米传民, 曾波, 李明珠, 徐盈婷. 纵横维度视角下的新型季节离散灰色预测模型及其应用[J]. 中国管理科学, 2025, 33(7): 178-186.

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.

图/表 9

图1

图2

表1

基于文献［11］基础产业用电量实例的建模结果（%）"

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

表1

表2

基于文献［4］月度GDP实例的建模结果（%）"

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

表2

表3

FDGM_SD∙PSO模型参数信息"

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

表3

表4

2013-2022年我国GDP季度数据模拟与预测信息"

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

表4

图3

表5

四个模型性能对比信息（%）"

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

表5

表6

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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