Research Article
A Hybrid Approach Integrating Multiple ICEEMDANs, WOA, and RVFL Networks for Economic and Financial Time Series Forecasting
Table 6
Results of the Diebold–Mariano (DM) test.
| | Dataset | Horizon | Tested Model | ICEEMDAN-LSSVR | ICEEMDAN-BPNN | ICEEMDAN-RW | LSSVR | BPNN | RW |
| | WTI | 1 | MICEEMDAN-WOA-RVFL | −4.9081 (≤0.0001) | −7.0030 (≤0.0001) | −6.1452 (≤0.0001) | −10.7240 (≤0.0001) | −10.3980 (≤0.0001) | −10.6210 (≤0.0001) | | ICEEMDAN-LSSVR | | −3.5925 (0.0003) | −6.0620 (≤0.0001) | −10.5640 (≤0.0001) | −10.3680 (≤0.0001) | −10.4660 (≤0.0001) | | ICEEMDAN-BPNN | | | −5.9718 (≤0.0001) | −10.2070 (≤0.0001) | −9.9529 (≤0.0001) | −10.0960 (≤0.0001) | | ICEEMDAN-RW | | | | 3.0776 (0.0021) | 2.7682 (0.0057) | 3.0951 (0.0020) | | LSSVR | | | | | −1.8480 (0.0648) | 1.0058 (0.3147) | | BPNN | | | | | | 1.9928 (0.0464) | | 3 | MICEEMDAN-WOA-RVFL | −4.9136 (≤0.0001) | −3.6146 (0.0003) | −10.8660 (≤0.0001) | −16.5990 (≤0.0001) | −15.6260 (≤0.0001) | −16.6720 (≤0.0001) | | ICEEMDAN-LSSVR | | −2.1143 (0.0346) | −10.7560 (≤0.0001) | −16.7020 (≤0.0001) | −15.6780 (≤0.0001) | −16.7760 (≤0.0001) | | ICEEMDAN-BPNN | | | −10.5250 (≤0.0001) | −16.2160 (≤0.0001) | −15.3500 (≤0.0001) | −16.2430 (≤0.0001) | | ICEEMDAN-RW | | | | 3.0818 (0.0021) | 2.0869 (0.0370) | 3.2155 (0.0012) | | LSSVR | | | | | −2.7750 (0.0056) | 2.3836 (0.0173) | | BPNN | | | | | | 3.0743 (0.0021) | | 6 | MICEEMDAN-WOA-RVFL | −3.9302 (≤0.0001) | −5.1332 (≤0.0001) | −18.9130 (≤0.0001) | −19.0620 (≤0.0001) | −21.9930 (≤0.0001) | −19.5080 (≤0.0001) | | ICEEMDAN-LSSVR | | −3.4653 (0.0005) | −18.9170 (≤0.0001) | −19.1680 (≤0.0001) | −22.0120 (≤0.0001) | −19.5420 (≤0.0001) | | ICEEMDAN-BPNN | | | −18.8380 (≤0.0001) | −19.1650 (≤0.0001) | −21.9930 (≤0.0001) | −19.5200 (≤0.0001) | | ICEEMDAN-RW | | | | 2.6360 (0.0085) | 0.5129 (0.6081) | 4.1421 (≤0.0001) | | LSSVR | | | | | −2.2124 (0.0271) | 3.9198 (≤0.0001) | | BPNN | | | | | | 4.3545 (≤0.0001) |
| | USD/EUR | 1 | MICEEMDAN-WOA-RVFL | −8.8860 (≤0.0001) | −8.6031 (≤0.0001) | −4.4893 (≤0.0001) | −15.4300 (≤0.0001) | −15.4100 (≤0.0001) | −15.3440 (≤0.0001) | | ICEEMDAN-LSSVR | | −0.8819 (0.3780) | −4.4230 (≤0.0001) | −14.7210 (≤0.0001) | −14.7320 (≤0.0001) | −14.6280 (≤0.0001) | | ICEEMDAN-BPNN | | | −4.4158 (≤0.0001) | −14.6310 (≤0.0001) | −14.6440 (≤0.0001) | −14.5310 (≤0.0001) | | ICEEMDAN-RW | | | | 3.3089 (0.0010) | 3.2912 (0.0010) | 3.3244 (0.0009) | | LSSVR | | | | | −1.8732 (0.06132) | 2.9472 (0.0033) | | BPNN | | | | | | 3.4378 (0.0006) | | 3 | MICEEMDAN-WOA-RVFL | −10.1370 (≤0.0001) | −7.9933 (≤0.0001) | −5.7359 (≤0.0001) | −18.3380 (≤0.0001) | −18.6460 (≤0.0001) | −18.2090 (≤0.0001) | | ICEEMDAN-LSSVR | | −1.4797 (0.1392) | −5.5972 (≤0.0001) | −17.9030 (≤0.0001) | −18.1920 (≤0.0001) | −17.7730 (≤0.0001) | | ICEEMDAN-BPNN | | | −5.6039 (≤0.0001) | −17.8370 (≤0.0001) | −18.1350 (≤0.0001) | −17.6910 (≤0.0001) | | ICEEMDAN-RW | | | | 3.0048 (0.0027) | 2.9552 (0.0032) | 3.0206 (0.0026) | | LSSVR | | | | | −1.4077 (0.1595) | 1.5242 (0.1278) | | BPNN | | | | | | 2.1240 (0.0339) | | 6 | MICEEMDAN-WOA-RVFL | −11.1070 (≤0.0001) | −10.0570 (≤0.0001) | −7.4594 (≤0.0001) | −18.3010 (≤0.0001) | −18.4640 (≤0.0001) | −18.4940 (≤0.0001) | | ICEEMDAN-LSSVR | | 1.9379 (0.0529) | −7.0858 (≤0.0001) | −17.4490 (≤0.0001) | −17.5970 (≤0.0001) | −17.6370 (≤0.0001) | | ICEEMDAN-BPNN | | | −7.1244 (≤0.0001) | −17.5850 (≤0.0001) | −17.7340 (≤0.0001) | −17.7690 (≤0.0001) | | ICEEMDAN-RW | | | | 2.5399 (0.0112) | 2.6203 (0.0089) | 2.6207 (0.0089) | | LSSVR | | | | | 2.2946 (0.0220) | 2.5913 (0.0097) | | BPNN | | | | | | −0.2090 (0.8345) | | IP | 1 | MICEEMDAN-WOA-RVFL | −3.4304 (0.0007) | −2.4253 (0.0098) | −3.4369 (0.0007) | −3.5180 (0.0005) | −4.1486 (≤0.0001) | −3.3215 (0.0015) | | ICEEMDAN-LSSVR | | −0.6714 (0.5026) | −3.2572 (0.0013) | −3.3188 (0.0010) | −4.0082 (≤0.0001) | −2.9573 (0.0034) | | ICEEMDAN-BPNN | | | −3.6265 (0.0004) | −3.7455 (0.0002) | −4.6662 (≤0.0001) | −3.3790 (0.0008) | | ICEEMDAN-RW | | | | −0.7438 (0.4577) | −0.0502 (0.9600) | 2.6089 (0.0096) | | LSSVR | | | | | 0.4094 (0.6826) | 3.4803 (0.0006) | | BPNN | | | | | | 1.6021 (0.1104) | | 3 | MICEEMDAN-WOA-RVFL | −4.5687 (≤0.0001) | −3.7062 (0.0003) | −5.9993 (≤0.0001) | −6.8919 (≤0.0001) | −5.5008 (≤0.0001) | −5.8037 (≤0.0001) | | ICEEMDAN-LSSVR | | 1.1969 (0.2325) | −5.5286 (≤0.0001) | −6.6325 (≤0.0001) | −5.2260 (≤0.0001) | −5.3260 (≤0.0001) | | ICEEMDAN-BPNN | | | −5.7199 (≤0.0001) | −6.7722 (≤0.0001) | −5.2955 (≤0.0001) | −5.5099 (≤0.0001) | | ICEEMDAN-RW | | | | −5.6536 (≤0.0001) | −3.6721 (0.0003) | 1.7609 (0.0795) | | LSSVR | | | | | 0.2479 (0.8044) | 6.3126 (≤0.0001) | | BPNN | | | | | | 3.9699 (≤0.0001) | | 6 | MICEEMDAN-WOA-RVFL | −5.9152 (≤0.0001) | −3.5717 (0.0004) | −5.9430 (≤0.0001) | −7.5672 (≤0.0001) | −10.8900 (≤0.0001) | −5.8450 (≤0.0001) | | ICEEMDAN-LSSVR | | −2.5163 (0.0125) | −5.8465 (≤0.0001) | −7.5185 (≤0.0001) | −10.7140 (≤0.0001) | −5.7483 (≤0.0001) | | ICEEMDAN-BPNN | | | −5.6135 (≤0.0001) | −7.4370 (≤0.0001) | −10.3470 (≤0.0001) | −5.5254 (≤0.0001) | | ICEEMDAN-RW | | | | −7.6719 (≤0.0001) | −2.2903 (0.02287) | 0.8079 (0.4200) | | LSSVR | | | | | 3.8137 (0.0002) | 7.7861 (≤0.0001) | | BPNN | | | | | | 2.3351 (0.0204) |
| | SSEC | 1 | MICEEMDAN-WOA-RVFL | −4.0255 (≤0.0001) | −3.748 (0.0004) | −7.9407 (≤0.0001) | −10.8090 (≤0.0001) | −10.3070 (≤0.0001) | −10.7330 (≤0.0001) | | ICEEMDAN-LSSVR | | −1.5083 (0.1317) | −7.8406 (≤0.0001) | −10.5410 (≤0.0001) | −10.0710 (≤0.0001) | −10.5020 (≤0.0001) | | ICEEMDAN-BPNN | | | −7.7986 (≤0.0001) | −10.5470 (≤0.0001) | −10.0580 (≤0.0001) | −10.5030 (≤0.0001) | | ICEEMDAN-RW | | | | 3.5571 (0.0004) | 3.2632 (0.0011) | 3.5150 (0.0005) | | LSSVR | | | | | −1.0197 (0.3081) | −0.6740 (0.5004) | | BPNN | | | | | | 0.8078 (0.4193) | | 3 | MICEEMDAN-WOA-RVFL | −3.8915 (0.0001) | −3.7312 (0.0002) | −10.5890 (≤0.0001) | −10.5480 (≤0.0001) | −10.7470 (≤0.0001) | −10.1260 (≤0.0001) | | ICEEMDAN-LSSVR | | −2.4145 (0.0159) | −10.5830 (≤0.0001) | −10.5240 (≤0.0001) | −10.7760 (≤0.0001) | −10.1110 (≤0.0001) | | ICEEMDAN-BPNN | | | −10.2420 (≤0.0001) | −10.1860 (≤0.0001) | −10.4400 (≤0.0001) | −9.7595 (≤0.0001) | | ICEEMDAN-RW | | | | 3.4031 (0.0007) | 2.3198 (0.0205) | 3.1912 (0.0014) | | LSSVR | | | | | −0.5931 (0.5532) | −1.2284 (0.2194) | | BPNN | | | | | | −0.0042 (0.9966) | | 6 | MICEEMDAN-WOA-RVFL | −2.9349 (0.0034) | −3.7544 (0.0002) | −10.2390 (≤0.0001) | −10.1970 (≤0.0001) | −11.0150 (≤0.0001) | −10.1630 (≤0.0001) | | ICEEMDAN-LSSVR | | −2.5830 (0.0099) | −10.1390 (≤0.0001) | −10.0940 (≤0.0001) | −10.9630 (≤0.0001) | −10.0690 (≤0.0001) | | ICEEMDAN-BPNN | | | −9.6418 (≤0.0001) | −9.5562 (≤0.0001) | −10.4090 (≤0.0001) | −9.5122 (≤0.0001) | | ICEEMDAN-RW | | | | 2.3167 (0.0207) | 1.3656 (0.1723) | 2.2227 (0.02639) | | LSSVR | | | | | −1.9027 (0.05728) | −0.5814 (0.5611) | | BPNN | | | | | | 1.5707 (0.1165) |
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