考虑空间邻近效应的经济时间序列预测建模与应用研究

doi:10.16381/j.cnki.issn1003-207x.2024.0854

Abstract

Abstract:

In real-world economic systems， the development trends of major systems are often influenced by spillover effects from neighbouring regions. However， existing grey multivariate models mainly focus on the temporal utility of correlated variables while overlooking the dynamic spatial relationships between neighbouring entities. To address this gap， a novel integrated spatial proximity term is introduced based on geographic and economic distances to measure spatial proximity effects. On this basis， three types of grey multivariate models that consider spatial proximity effects have been developed， namely STGM（1， N， M）， STGMC（1， N， M）， and STDGM（1， N， M） models. Moreover， the challenge of selecting model hyperparameters is tackled by designing an innovative intelligent algorithm selection framework. This framework introduces three criteria for identifying optimal algorithms， including accuracy verification， statistical testing， and parameter sensitivity analysis， thus enhancing the reliability， stability， and interpretability of the model solutions. The effectiveness and applicability of the spatial proximity term are validated through various methods， such as the HLN test， Monte-Carlo simulations， and probability density analysis， from the perspectives of accuracy and stability. Finally， a case study on the economic prediction of Shanghai demonstrates that the integration of the novel spatial proximity term significantly improves the ability of all three grey multivariate models to capture the spatial proximity effects of neighbouring regions， offering enhanced prediction accuracy， reliability， and stability.

Key words: grey system, grey multivariable models, spatial proximity effects, grey forecasting

CLC Number:

N941.5

Song Ding,Xingao Shen,Yaoguo Dang, et al. Modelling and Application of Economic Time Series Forecasting Considering Spatial Proximity Effect[J]. Chinese Journal of Management Science, 2026, 34(4): 34-46.

Figures/Tables 13

模型	$ξ 1$	$ξ 2$	$ξ 3$	$a 1$	$a 2$	$a 3$	$a 4$	$a 5$	$a 6$	$a 7$
STGM(1,3,3)	1.000	1.000	0.999	2.447	0.372	-0.025	0.732	0.570	5.557	—
STGMC(1,3,3)	0.968	0.659	0.987	-0.007	0.014	0.015	0.509	-0.538	-1.146	417.166
STDGM(1,3,3)	0.000	1.000	0.295	-0.117	0.057	0.002	0.060	0.844	-0.139	74.215

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模型	基准算法	候选算法	DM检验		Wilcoxon检验
模型	基准算法	候选算法	DM值	P值	P值
STGMC (1, 3, 3)	PSO	GWO	-55.9186	0.0000	0.0000
		WOA	-10.6447	0.0000	0.0000
		ALO	-16.1185	0.0000	0.0000
STDGM (1, 3, 3)	WOA	PSO	-3.1964	0.0014	0.0090
		GWO	-4.8209	0.0000	0.0000
		ALO	-42.5222	0.0000	0.0000
STGM (1, 3, 3)	WOA	PSO	-8.0086	0.0000	0.0000
		GWO	-6.1543	0.0000	0.0000
		ALO	-16.9115	0.0000	0.0000

组别	惯性系数w	加速度因子c₁	加速度因子c₂
组1	0.40000	2.00000	2.00000
组2	0.72900	1.49445	1.49445
组3	0.60000	1.70000	1.70000
组4	0.50000	1.00000	1.00000

	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011
江苏	0.0018	0.0009	0.0005	0.0007	0.0006	0.0005	0.0002	0.0008	0.0047	0.0051	0.0023
浙江	0.0008	0.0012	0.0014	0.0018	0.0014	0.0022	0.0012	0.0025	0.0088	0.0137	0.0063
安徽	0.0001	0.0001	0.0000	0.0000	0.0000	0.0000	0.0000	0.0041	0.0173	0.0142	0.0054
	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021
江苏	0.0054	0.0583	0.0542	0.0031	0.0076	0.0020	0.0005	0.0009	0.0004	0.0005
浙江	0.0093	0.0238	0.0244	0.0208	0.0213	0.0027	0.0021	0.0022	0.0007	0.0007
安徽	0.0143	0.1326	0.1584	0.0282	0.0389	0.0065	0.0025	0.0004	0.0001	0.0002

年份	观测值	SPDGM(1,3,3)	STGM(1,3,3)	GM(1,3)	STGMC(1,3,3)	GMC(1,3)	STDGM(1,3,3)	DGM(1,3)
2001	525.77	525.77	525.77	525.77	525.77	525.77	525.77	525.77
2002	579.50	525.64	491.84	482.25	579.50	608.63	580.13	589.71
2003	680.40	642.23	684.11	895.56	685.10	698.19	680.13	678.39
2004	810.16	761.22	811.12	1114.13	798.32	804.06	810.16	798.90
2005	919.71	898.24	924.53	1251.39	932.80	929.42	925.60	940.98
2006	1059.89	1014.53	1052.95	1358.70	1087.08	1069.06	1067.55	1062.70
2007	1287.87	1165.98	1251.29	1512.78	1250.12	1224.84	1271.47	1221.67
2008	1453.69	1387.34	1423.54	1672.26	1426.22	1397.01	1443.66	1455.92
2009	1574.24	1555.68	1580.66	1787.91	1612.91	1582.27	1560.35	1631.37
2010	1791.54	1669.17	1781.86	1946.27	1791.54	1773.99	1794.45	1757.65
2011	2000.97	1857.45	1958.72	2180.93	1972.07	1961.72	2015.62	1969.86
2012	2130.56	2056.68	2115.85	2403.49	2158.53	2149.35	2167.03	2186.21
2013	2320.41	2194.38	2331.51	2615.79	2320.97	2347.84	2323.29	2334.86
2014	2526.98	2384.06	2514.60	2840.03	2498.68	2559.91	2465.67	2538.52
2015	2688.70	2583.36	2690.77	2967.98	2728.03	2782.17	2772.39	2747.65
2016	2988.70	2751.18	2927.12	3227.31	2973.56	3015.45	2935.72	2929.77
2017	3292.50	3044.00	3243.89	3502.83	3292.50	3264.99	3293.08	3241.51
2018	3601.18	3336.34	3587.62	3805.20	3598.91	3530.41	3572.48	3555.80
拟合期MAPE（%）		5.45	1.80	16.60	1.14	1.95	0.89	1.71
拟合期RMSE		134.08	33.23	245.95	22.29	40.50	31.26	38.74
2019	3798.76	3633.59	3828.71	4111.62	3810.79	3809.81	3848.18	3875.22
2020	3896.33	3847.29	4043.91	4287.46	4039.72	4108.00	4015.64	4094.51
2021	4321.49	3975.32	4539.83	4631.47	4268.77	4430.73	4480.92	4234.94
预测期MAPE（%）		4.54	3.21	8.48	1.74	2.75	2.68	3.03
预测期RMSE		223.24	153.14	340.08	88.48	137.67	118.46	132.43

模型		STGM (1,3,3)	GM (1,6)	STGMC (1,3,3)	GMC(1,6)	STDGM (1,3,3)	DGM(1,6)
预测指标		STGM (1,3,3)	GM (1,6)	STGMC (1,3,3)	GMC(1,6)	STDGM (1,3,3)	DGM(1,6)
样本内	MAPE(%)	1.80	1.80	1.14	3.28	0.89	1.16
样本内	RMSE	33.23	33.19	22.94	48.08	31.26	18.50
样本外	MAPE(%)	3.21	3.32	1.74	5.32	2.68	4.10
样本外	RMSE	153.14	157.08	88.48	224.12	118.46	230.78

Modelling and Application of Economic Time Series Forecasting Considering Spatial Proximity Effect

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改进模型	传统模型	HLN检验	P值
STGM(1,3,3)	GM(1,3)	-12.6166^***	0.0000
STGMC(1,3,3)	GMC(1,3)	-2.3161^**	0.0313
STDGM(1,3,3)	DGM(1,3)	-2.1456^**	0.0444

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