A New Conformable Fractional-Order Time-Delay Grey Bernoulli Model with the Arithmetic Optimization Algorithm and Its Application in Rural Regional Economy

Table 4

The evaluation indicators of the ten models in two cases.

	CFTDNGBM	FDGM	FNDGM	FDGMP	FDGM (1, 1, t^α)	FGDGMP	WDGM	FTDGM	LSSVR	CFDGM (1, 1)
RRCL
Train
MAPE	1.3620	1.7806	1.4525	1.4630	1.3943	1.4096	1.7957	1.5495	2.4392	2.6191
RMSE	94.8849	103.8036	99.0455	101.7698	97.9779	98.6626	119.3347	105.4968	160.6342	130.8161
R^2	0.9977	0.9972	0.9975	0.9974	0.9975	0.9975	0.9968	0.9971	0.0332	0.0295
rRMSE	0.0214	0.0234	0.0223	0.0230	0.0221	0.0223	0.0269	0.0238	116.2264	103.3162
MAE	62.1315	76.0923	69.7769	73.0246	68.1469	68.6023	75.6808	76.4423	0.9981	0.9989
IA	0.9994	0.9993	0.9994	0.9993	0.9994	0.9994	0.9991	0.9993	25803.3463	17112.8593
MSE	9003.1358	10775.1772	9810.0136	10357.0824	9599.6754	9734.3096	14240.7803	11129.5774	2.4392	2.6191
Test
MAPE	2.3113	3.1480	6.6800	9.6739	5.4340	6.7895	3.8925	17.1083	5.5442	2.5684
RMSE	453.1107	821.3741	1359.0174	1824.4150	1103.7555	1353.0515	910.2267	3434.1013	964.5873	510.6199
R^2	0.9788	0.9666	0.9636	0.9613	0.9681	0.9643	0.9661	0.9331	0.0746	0.0395
rRMSE	0.0351	0.0635	0.1051	0.1411	0.0854	0.1047	0.0704	0.2656	794.8417	369.8183
MAE	327.0333	470.0250	964.6383	1383.1333	777.8067	975.2067	566.1450	2503.6217	0.9523	0.9898
IA	0.9908	0.9762	0.9431	0.9082	0.9596	0.9433	0.9713	0.7861	930428.6440	260732.6682
MSE	205309.3459	674655.4052	1846928.2315	3328490.0677	1218276.2584	1830748.4720	828512.7178	11793051.9895	5.5442	2.5684
RRPCCEX
Train
MAPE	1.0008	1.2976	1.2325	1.0481	1.2160	1.1185	1.2500	1.3130	1.5513	1.2496
RMSE	70.0404	90.7675	98.4981	76.3337	82.4327	88.7683	86.6319	93.3950	108.1011	89.4319
R^2	0.9990	0.9984	0.9982	0.9989	0.9987	0.9985	0.9985	0.9983	0.0197	0.0179
rRMSE	0.0140	0.0182	0.0198	0.0153	0.0165	0.0178	0.0174	0.0187	78.6891	68.7715
MAE	51.6080	70.8369	69.8069	56.2285	62.2608	63.2800	66.0585	70.5546	0.9993	0.9996
IA	0.9998	0.9996	0.9995	0.9997	0.9997	0.9996	0.9996	0.9996	11685.8522	7998.0700
MSE	4905.6618	8238.7322	9701.8670	5826.8320	6795.1469	7879.8179	7505.0835	8722.6162	1.5513	1.2496
Test
MAPE	3.5174	12.8543	15.7291	6.4070	6.7780	12.7090	10.2211	13.2455	12.5090	12.3202
RMSE	557.2025	2024.5019	2444.3165	953.9553	1044.7826	1966.8477	1606.1281	2180.2284	2275.6704	1936.7940
R^2	0.9736	0.9775	0.9776	0.9748	0.9757	0.9774	0.9772	0.9780	0.1793	0.1526
rRMSE	0.0439	0.1595	0.1926	0.0752	0.0823	0.1549	0.1265	0.1718	1756.0850	1663.0717
MAE	449.3749	1736.5667	2119.8250	840.3600	901.1633	1708.6450	1377.1817	1810.1883	0.6031	0.8518
IA	0.9797	0.8427	0.7969	0.9483	0.9412	0.8471	0.8865	0.8306	5178675.7793	3751171.0137
MSE	310474.6518	4098607.7344	5974683.2700	910030.7244	1091570.6801	3868489.9384	2579647.5880	4753395.7882	12.5090	12.3202