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Weather Average0.031 0.056 ：|0.0470.1270.0300.054 0.0490.132|0.0340.0760.1710.1170.0520.1100.099 0.2030.032 [0.060 0.144|0.1970.309|0.1230.228|0.1190.224|0.1120.229|0.0560.142|0.0610.151|0.1650.273|0.134 0.2400.059 0.0310.0570.0450.1040.0380.087
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MethodsGPT2(6) MSE MAETimesNet MSEMAEETSformer MSE MAELightTS MSEMAEDLinear MSEMAEFEDformer MSEMAEPatchTST MSE MAEStationary MSEMAEAutoformer MSEMAEInformer MSE MAEReformer MSE MAE
Weather ETTh1 ETTh2 ETTm10.2370.270 0.427 0.426 0.3460.394 0.352 0.3830.2590.287 0.4580.450 0.4140.427 0.400 0.406 0.2910.439 0.4290.271 0.334 0.5420.510 0.452 0.425[0.261 0.312 0.491 0.479 0.602 0.543 0.435 0.4370.2490.300 0.4230.437 0.431 0.3570.447 0.378 0.3340.3090.360 0.4400.460 0.437 0.449 0.448 0.4520.2250.264 0.413 0.430 0.330 0.379 0.351 0.3870.288 0.314 0.5700.537 0.5260.516 0.4810.4560.3380.382 0.4960.487 0.450 0.459 0.588 0.51710.6340.548 1.040 0.795 4.431 0.9611.729 0.734 0.7990.8030.656 1.0290.915 6.7362.191 0.671
ETTm2 ILI ECL Traffic0.2660.326 1.9250.903 0.1670.263 0.414 0.2940.333 2.139 0.931 0.1920.295 0.620 0.336 |0.5960.433|0.293 2.497 0.621 |0.662 0.473|1.303 0.616|0.562 0.436|0.701 0.489|0.342 1.004 0.2080.323 0.3960.409 0.436 7.382 2.003 0.229 0.329 0.622 0.3920.267 2.169 0.166 0.4340.305 1.041 2.847 50.263 0.295 0.6100.349 1.144 0.214 0.327 0.3760.255 0.315 1.4430.798 0.161 0.253 0.390 0.264 |0.4460.386|0.6330.465|0.757 0.511|0.306 2.077 0.1930.296 0.6240.347 0.327 0.914 3.006 0.227 0.340 0.6280.371 1.161 0.338 0.3791.410 5.137 1.544 0.311 0.397 0.764 0.4160.810 1.479 4.724 0.7410.915 1.445 0.3380.422 0.422
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MethodsGPT2(6) OursTimesNet PatchTS.ETS.FED.LightTS DLinear StationaryAuto.In.Re.LogTrans.Trans.
SMD86.8984.6184.6283.1385.0882.5377.1084.7285.1183.0485.4981.6575.3276.2179.56
MSL82.4581.8478.7085.0378.5778.9584.8877.5079.0584.8683.3184.0684.4079.5778.68
SMAP72.8869.3968.8269.5070.7669.2169.2671.0971.12 71.0971.1869.92 70.4069.9769.70
SWaT94.2393.0285.7284.9193.1993.3387.5279.8892.7491.7883.1081.43 82.8080.5280.37
PSM97.1397.3496.0891.7697.2397.1593.5597.2993.2982.0879.4077.10 73.6176.7476.07
Average86.7285.2482.7982.87 84.9784.2382.4682.0884.26 82.5780.5078.8377.3176.6076.88
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MethodsGPT2(6) MSE MAETimesNet MSE MAEDLinear MSE MAEFEDformer MSEMAEPatchTST MSEMAEAutoformer MSE MAEStationary MSE MAEETSformer MSE MAELightTS MSE MAEInformer MSE MAEReformer MSE MAE
Weather ETTh1 ETTh20.238 0.275 0.5900.524 0.3970.4210.279 0.301 0.869 0.628 0.479 0.4650.301 0.283 0.691 0.599 0.608 0.5380.2840.324 0.638 0.561 0.4660.4750.241 0.6330.542 0.415 0.4310.27910.3000.342 0.701 0.596 0.4880.4990.318 0.322 0.9140.639 0.4610.4540.317 0.359 1.179 0.833 0.8930.7130.289 0.322 1.375 0.877 2.6550.597 1.199 0.8080.4940.545 0.469 1.249 0.833
ETTm1 ETTm20.4640.441 0.2930.3350.676 0.537 0.319 0.3530.4110.429 0.3160.3680.721 0.605 0.463 0.4880.501 0.296 0.3430.466 0.8020.628 0.9300.797 0.3320.577 0.979 0.714 0.4470.4871.159 0.970 0.7043.871 1.192 3.3691.512 3.485 0.820 1.4251.485 0.856
ECL0.1760.2690.323 0.3920.2800.3460.4280.180 0.2691.3410.4780.366 0.4430.987 0.4410.755 0.4881.439 1.194 0.8903.9771.586 50.768
0.9510.5350.1800.4250.4310.479 0.8150.659 0.6170.965
Traffic Average0.4400.3090.496 0.3710.663 |0.3710.367|0.556 0.458|0.429 0.409|0.511 0.472|0.4300.305 0.3850.3760.7490.446 [0.687 0.559|0.674 0.522|0.912 0.665|1.137 0.712|1.850 0.967|1.888 0.9741.4531.913 0.9361.2470.6841.5340.8111.550 0.821
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Methods ||GPT2(6)TimesNetPatchTSTN-HiTS N-BEATSETSformerLightTSDLinearFEDformer StationaryAutoformer InformerReformer
SMAPE11.99111.82912.05911.92711.85114.71813.52513.63912.84012.78012.90914.08618.200
MASE1.6001.5851.6231.6131.5992.4082.1112.0951.7011.7561.7712.7184.223
OWA0.8610.8510.8690.8610.8551.1721.0511.0510.9180.9300.9391.2301.775
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Methods MetricM4 sMAPEM3 sMAPETOURISM MAPEELECTR ND×100Average
N-BEATS11.7012.4418.8217.815.19
DLinear15.3314.0328.5117.618.86
TimesNet13.5514.1728.8419.318.96
PatchTST13.2213.0627.1017.317.67
ETSformer27.7416.03180.4044.267.09
LightTS13.6217.9066.9919.629.52
Stationary13.3215.2943.7522.023.59
FEDformer15.0413.5331.5518.419.63
Autoformer20.0215.8740.3933.927.54
Informer19.0415.8235.8221.222.97
Reformer14.0913.3725.4821.618.63
GPT2(6)13.1213.0622.1417.216.38
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MethodsGPT2(6)GPT2(0)No FreezeNo Pretrain
MSEMAEMSEMAEMSEMAEMSEMAE
Weather0.2370.2700.2630.2970.2730.3020.2770.305
ETTh10.4270.4260.8740.6470.7530.5961.3260.743
ETTh20.3460.3940.6660.5590.4470.4510.5020.479
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MethodsGPT2(6)BERT(6)BEiT(6)DLinearPatchTSTFEDformerAutoformer
MSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
ETTh20.4000.4330.4520.4510.4590.4540.8270.6150.4390.4480.4410.4570.4700.489
ETTm20.3080.3460.3180.3570.3150.3570.3990.4260.3140.3520.3810.4040.3880.433
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ModelTraining Params Training Params Percentages Training Time for l step(s） Inference Time for 1 Batch(s)
FEDformer-3244k1000.8890.170
TimesNet-322M1000.7470.302
PatchTST-32543K1000.0430.022
FEDformer-76833M1000.2080.056
TimesNet-76842M1005.7232.162
PatchTST-76820M1000.4570.123
GPT-2(3)-7684M6.120.0930.032
GPT-2(6)-7684M4.60.1040.054
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M3 Monthly142818Monthly
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M4 Quarterly240008Quarterly
M4 Monthly4800018Monthly
M4 Weekly35913Monthly
M4 Daily422714Monthly
M4 Hourly41448Monthly
TOURISM Yearly5184YearlyYearly
TOURISMQuarterly4278QuarterlyQuarterly
TOURISMMonthly36624MonthlyMonthly
ELECTR1311168HourlyMonthly
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MethodsGPT2(6)GPT2(0)DLinearPatchTSTTimesNetFEDformerAutoformerStationaryETSformerLightTSInformerReformer
MetricMSEMAE|MSEMAE MSEMAE|MSEMAEMSEMAE|MSE MAEMSE MAEMSEMAEMSEMAE|MSEMAEMSEMAE|MSEMAE
96 0.1750.230 0.191 0.2760.243 0.2440.28910.184 0.242 0.2280.28310.171 0.224 0.2300.2770.207 0.253 0.272 0.307[0.2290.309 0.2650.3170.227 0.299 0.278 0.3330.215 0.2900.2520.218 0.2950.230 0.2850.4970.497[0.406 0.435
Waaeet192 0.227 336 0.2860.322 720 0.3660.379 0.3910.3030.332 0.3930.2790.322 0.364 40.3880.2940.326 0.384 0.3870.313 0.328 0.400 0.3850.3530.392 0.391 0.3940.351 0.393 0.387 0.3890.353 0.4520.307 0.348 0.4070.2940.331 0.3590.398 0.461 0.4610.2740.323 0.3180.355 0.4010.4180.620 0.545 0.6490.547 0.570 0.5220.4460.450 0.4650.459 0.471 0.468
Avg. 0.263 96 0.5430.5060.3010.2820.314 0.8250.6380.2630.308 0.5470.5030.2690.303 0.5570.5190.298 0.318 0.892 0.6250.3090.353 0.5930.5290.310 0.353 0.6810.5700.327 0.9520.6500.3280.333 0.371 1.169 0.8320.305 0.345 1.483 0.910.5840.527 1.2250.8120.4470.453 1.1980.795
LLI192 0.7480.580 336 0.7540.595 7201.2200.7781.852 0.9650.7200.604 0.9840.7270.711 0.570 0.8160.6190.940 0.665 0.9450.6530.652 0.563 0.7310.5940.7250.602 0.761 0.6240.9430.645 0.9350.6441.221 0.853 1.1790.8321.525 0.93 1.347 0.871.249 0.828 1.202 0.8111.2730.853 1.2540.857
Avg. 0.6810.5601.2990.793 0.551 0.5070.750 0.611 10.4420.4560.6940.569 0.4010.4210.9250.647 0.409 0.4200.658 0.562 |0.390 0.4240.722 0.5980.9430.6461.189 0.8391.451(0.903 1.2250.8171.241 0.835
LLI96 [0.376 0.421 192 0.418 0.4410.7650.610 0.6170.5420.452 0.4550.4830.4640.457 0.4650.4280.468 0.4960.5040.4080.423 0.4970.6780.619 0.6972.0221.006 3.837 3.9751.5083.7531.518 3.5161.473
336 0.4080.4390.7670.6141.424 0.8490.4640.4690.499 0.4790.477 0.4830.486 0.4960.507 0.4810.4680.845 0.9050.7273.5341.3481.933 3.9561.5203.3121.427
7204.0631.451
Avg. 0.4000.4330.6940.5770.8270.6150.4390.4480.4630.4540.4410.4570.47 0.4890.470 0.4573.527 1.472
0.5820.512 0.3320.3740.3990.4140.606 0.5180.6280.54450.5780.809 0.6813.2061.268 3.9221.653
96 0.386 0.405 0.4400.4380.6320.5360.3580.3900.4410.4360.681 0.5390.6660.5660.7260.8230.5871.031 0.7471.0480.7331.130 0.7751.2340.798
LL192 336 0.4850.4590.7670.5840.4020.4160.4990.4670.7860.5970.8070.6280.7500.591 0.8510.8440.591 0.8700.6031.0870.7661.0970.7561.150 0.7881.287 0.839
720 0.5770.499 1.3340.7420.5110.4890.767 0.5870.7960.5930.8220.6330.659 0.857 0.6550.8930.6111.1380.7871.1470.7751.198 0.8091.2880.842
Avg. 0.472 0.4500.828 0.5930.4000.4170.5260.4760.717 0.5610.730 0.5920.7960.6200.8571.2450.8311.200 0.7991.175 0.7941.2470.828
0.5981.1250.7821.1230.7651.1630.7911.2640.826
96 [0.1990.280[0.282 0.347 0.3460.3830.236 0.3260.2060.288[0.220 0.299|[0.229 0.3200.232 0.3220.2380.3160.4040.4851.1080.7723.5991.4783.883 1.545
192 0.2560.3160.4290.4270.3060.373 0.3800.4230.2640.3240.311 0.3610.3940.3610.291 0.3570.2980.3490.4790.5211.317 0.8503.5781.4753.5531.484
L336 0.3180.3530.751 0.5680.6740.5830.334 0.3670.338 0.3660.378 0.4270.478 30.5170.353 0.3800.552 0.5551.415 0.8793.5611.4733.4461.460
720 0.460 0.4360.4520.4310.4540.4320.5090.4650.523 0.5100.553 0.5380.4750.4450.7010.6271.8220.9843.8961.5333.4451.460
Avg. 0.3080.3460.3990.4260.314 0.3520.3440.3720.381 0.4040.388 30.4330.3410.3720.5340.5471.4150.8713.6581.4893.5811.487
96 [0.1430.241[0.1470.2460.1500.2510.1450.2440.315 0.389[0.235 0.3220.2970.3670.4840.518
GCI192 0.159 0.2550.1630.2600.1630.2630.163 0.2600.318 0.3960.2470.3410.3080.3750.501 0.5310.697 0.63810.639 0.6091.265 0.9191.4140.855
0.1820.2780.1750.2780.2810.3400.4150.267 0.3560.3540.4110.5740.7180.6480.772 0.6781.298 0.9391.2400.919
336 0.1790.2740.2190.3110.1830.4260.4660.9520.7860.5780.758 0.6670.9010.7451.3020.9421.2530.921
720 0.2330.3230.2390.3290.2330.3230.6350.6130.3180.3940.3460.4040.6271.0280.7881.2000.8711.2590.919 1.281 0.9291.2490.921 1.2890.904
mffoiAvg. 0.1780.2730.1820.278 0.419 0.2980.4680.354 10.4270.1760.275 0.3040.181 0.277 0.4040.2860.402 0.453 0.8540.4920.266 0.353 [0.6700.4210.7950.481 0.8370.5031.4680.8210.603 1.6430.8550.800 0.6850.878 0.725 1.1570.636
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MethodsGPT2(6)GPT2(0)DLinearPatchTSTTimesNetFEDformerAutoformerStationaryETSformerLightTSInformerReformer
MetricMSEMAEMSE MAEMSEMAE MSEMAE MSEMAE|MSEMAE|MSEMAEMSEMAE| MSEMAE|MSE MAE||MSE MAE|MSEMAE
96 0.163（0.215 0.1900.2400.171 0.2240.165 0.2150.184 0.2300.1880.2530.221 0.2970.192 0.2340.1990.272 10.2170.2690.3740.4010.3350.380
192 0.2100.2540.2430.2840.215 50.2630.2100.2570.245 0.2830.2500.3040.2700.3220.2690.295 0.2790.332 0.2590.3040.5520.4780.5220.462
Waaeet336 0.2560.2920.270 0.3050.258 0.2990.259 0.2970.305 0.3210.312 0.3460.320 0.3510.370 0.3570.356 0.3860.3030.3340.7240.5410.7150.535
720 0.321 0.3390.348 0.3590.320 0.3460.332 0.3460.381 0.3710.387 0.3930.390 0.3960.4410.405 0.4370.448 0.3770.3820.7390.5580.611 0.500
Avg. 0.238 0.2750.263 0.2970.241 0.2830.242 0.2790.279 0.3010.284 0.3240.3000.3420.318 0.3230.3180.3600.2890.3220.597 0.4950.5460.469
96 0.4580.4560.601 0.5360.4920.4950.5160.4850.861 0.6280.5120.4990.6130.5520.9180.6391.1120.8061.2980.8381.1790.7921.1840.790
LLI192 0.570 0.5160.7090.587 0.535 0.8010.565 0.5380.598 0.5240.797 0.5930.624 0.5550.722 0.5980.9150.629 1.1550.823 1.3220.8541.199 0.8061.2950.850
336 0.6081.3850.8310.635 0.721 0.6220.657 0.5500.941 0.6480.691 0.5740.750 0.6190.9390.644 1.1790.832 1.3470.8701.202 0.8111.2940.854
720 0.7250.591 0.5900.5250.8740.6470.986 0.7430.762 0.6100.877 0.6410.7280.6140.721 0.6160.8870.645 1.2730.874 1.5340.9471.2170.8251.2230.838
Avg.0.691 0.6000.633 0.5420.869 0.6280.6390.5610.702 0.5960.9150.639 1.180 0.8341.3750.8771.199 0.8091.2490.833
96 0.3310.374 0.5390.4950.357 0.4110.353 0.3890.378 0.409[0.382 0.4160.413 0.4510.3890.4110.6780.6192.0221.0063.837 1.5083.788 1.533
LLE192 0.4020.411 0.6750.5550.569 0.5190.4030.4140.490 0.4670.4780.4740.4740.4770.4730.455 0.7850.6662.3291.1043.856 1.5133.552 1.483
336 0.4060.4330.718 0.5800.671 0.5720.4260.4410.5370.4940.5040.5010.547 0.5430.5070.4800.8390.6942.4531.1223.952 1.5263.395 1.526
720 0.4490.464 Avg. 0.3970.4210.732 0.6050.824 0.6480.477 0.4800.5100.4910.4990.5090.5160.5230.4770.472 1.2730.8743.8161.4073.842 1.5033.205 1.401
0.6660.5590.605 0.5380.415 0.4310.4790.4650.4660.4750.4880.4990.4620.455 0.8940.713 2.6551.1603.872 1.5133.485 1.486
L96 0.390 0.404[0.610 0.5080.352 0.392[0.410 0.4190.583 0.5010.578 0.518[0.7740.6140.7610.568 0.9110.688 0.9210.6821.162 0.7851.4420.847
192 0.4290.423 336 0.4690.4390.6660.5400.3820.4120.437 0.4340.630 0.5280.6170.5460.7540.5920.7810.574 0.9550.703 0.9570.7011.1720.7931.4440.862
720 0.5690.4980.895 0.615 0.9160.6460.419 0.4340.476 0.4540.7250.5680.9980.7750.8690.6770.8030.587 0.9910.719 0.9980.7161.227 0.9081.450 0.866
Avg. 0.4640.4410.7720.5770.4900.4770.681 0.5560.769 0.5490.6930.579 0.722 0.6050.810 0.6300.844 0.5811.0620.747 1.0070.7191.207 0.7971.366 0.850
96 [0.1880.2690.411 0.4290.501 0.4660.677 0.5370.802 0.6280.797 0.5780.980 0.7140.9710.7051.192 0.8211.4260.856
L192 0.251 0.3090.2830.3440.2130.3030.191 0.2740.212 0.2850.291 0.39910.3520.4540.2290.3080.3310.430 0.8130.6883.2031.4074.1951.628
336 0.3070.3460.353 0.3840.278 0.3450.252 0.3170.270 0.3230.3070.3790.694 0.6910.291 0.3430.400 0.4641.0080.7683.112 1.3874.042 1.601
720 0.4260.4170.4200.4220.3380.3850.306 0.3530.323 0.3530.5430.5592.408 1.4070.348 0.3760.4690.498 1.0310.7753.255 1.4213.963 1.585
0.2930.3350.5530.4910.4360.4400.433 0.4270.4740.4490.7120.6141.913 1.1660.461 0.4380.5890.5571.0960.7913.9091.5433.7111 1.532
Avg.0.4020.4100.3160.3680.296 0.3430.320 0.3530.4630.4881.342 0.9300.332 0.3660.4470.4870.9870.7563.370 1.4403.978 1.587
96 [0.139 0.2370.142 0.2400.1500.2530.140 0.2380.2990.3730.231 0.3230.261 0.3480.420 0.4660.5990.5870.3500.425
ECE192 0.1560.2520.1580.2540.164 0.2640.160 0.2550.3050.3790.261 0.3560.338 0.4060.411 0.4590.620 0.5980.3760.4481.259 0.9190.9930.784
336 0.1750.2700.1750.2710.181 0.2820.180 0.2760.319 0.3910.360 0.4450.410 0.4740.4340.4730.6620.6190.4280.4851.1600.873 1.1570.8720.938 0.753 0.925 0.745
720 0.2330.3170.2300.3150.2230.321 0.180 0.2800.241 0.323 0.180 0.2730.369 0.426 0.323 0.3920.5300.585 0.3460.4270.7150.685 0.431 0.4780.510 0.521 0.4440.4800.7570.664 0.6600.6170.611 0.4410.597 0.489 1.1950.8911.2030.8981.0040.790
TffoosAvg. 0.1760.269 96 0.4140.2970.1760.270 0.478 0.368
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Methods |GPT2(6)GPT2(0) DLinearPatchTSTTimesNetFEDformerAutoformer StationaryETSformerLightTSInformerReformer
MetricMSEMAE|MSEMAEMSE MAEMSEMAEMSEMAEMSEMAE|MSEMAEMSEMAE|MSEMAEMSEMAEMSEMAE
96 0.162 0.20420.212 0.181 0.248 0.2220.232 0.2660.176 0.2200.237 0.149 0.198 0.2820.1720.220 0.2190.2610.217 0.296 0.2760.3360.2660.336MSEMAE| 0.173 0.223[0.197 0.2810.1820.242 0.3000.3840.689 0.596
Wareet192 336 7200.2540.286 0.3260.3370.270 0.299 0.338 0.3450.2650.319 0.3330.3620.1940.241 0.2450.282 0.3140.3340.2800.306 0.3650.3590.403（0.3390.380 0.4280.307 0.3590.395 0.4190.4280.367 0.2450.285 0.321 0.338 0.4140.4100.237 0.312 0.2980.353 0.3520.2880.227 0.287 0.282 0.334 0.352 20.3860.5980.544 0.578 0.523 1.0590.7410.7520.638 0.639 0.5961.1300.792
Avg 960.2370.270 0.3760.397 0.4160.4180.252 0.422 0.4660.285 0.428 0.3750.248 0.300 0.3990.2250.264 0.3700.3990.3840.259 0.287 0.402 0.4360.4290.420（0.309 0.360 [0.376 0.4190.338 0.3820.4490.4590.288 0.314 0.513 0.4910.271 0.334 0.494 0.4790.261 0.312 10.424 40.4320.6340.548 0.8650.7130.8030.656 0.837 0.728
ULL192 336 720 Avg0.4420.433 0.4770.456 0.427 0.4260.450 0.488 0.464 0.485 0.478 0.465 0.4550.405 0.4220.416 0.4390.443 0.4720.490 0.4370.413 0.421 0.4220.436 0.4470.466 0.413 0.4300.5210.491 0.469 0.500 0.4580.4500.448 0.4590.465 0.506 0.507 0.4400.4600.5000.482 0.521 0.496 0.514 0.512 0.4960.4870.5340.504 0.5880.535 0.643 0.6160.5380.504 0.5740.521 0.562 0.5350.4750.462 0.518 30.488 0.547 0.5331.0080.792 1.107 0.809 1.181 0.8650.9230.766 1.0970.8351.257 0.889
TLL96 192 3360.2850.342 0.3540.389 0.3730.4070.318 0.368 0.383 0.407 0.4060.4270.2890.353 0.3830.418 0.4480.4650.274 0.336 0.3390.379 0.3290.3800.4520.340 0.374 0.4020.414 0.4520.3580.397 0.4290.439 0.4960.4870.346 0.388 0.4560.452 0.4820.4860.5520.5700.537 0.476 0.458 0.5120.493 0.5510.5420.510 0.340 0.391 0.4300.439 0.4850.4790.491 0.479 10.397 0.437 0.520 0.504 0.6260.5591.0400.795 3.755 1.525 5.6021.9311.029 0.805 2.626 1.31711.12 2.979 9.3232.769
720 Avg 96 1920.4060.441 0.3540.394 0.2920.346 0.3320.3720.420 0.381 0.3300.446 0.412 0.372 0.3940.605 0.551 0.431 0.446 0.2990.3430.3790.422 0.3300.379 0.290 0.3420.462 0.468 0.4140.427 0.3380.375 0.3740.3870.4630.474 0.4370.449 0.3790.4190.515 0.511 0.450 0.459 0.5050.4750.5620.560 0.526 0.516 0.386 0.3980.5000.497 0.4390.452 0.3750.3980.8630.672 0.602 20.543 10.374 0.4004.721 3.647 4.431 0.672 0.5711.835 1.625 3.8741.697 1.729 6.736 2.1910.538 0.528
L336 720 Avg0.3660.394 0.417 0.421 0.3520.3830.371 0.398 0.454 0.3880.409 0.440 0.403 0.3570.3350.365 0.369 0.386 0.4250.421 0.3780.3320.369 0.3660.392 0.4160.420 0.351 0.3800.410 0.411 0.4780.450 0.4000.4060.4260.441 0.4450.459 0.5430.490 0.4480.4520.5530.496 0.621 0.671 0.588 0.5170.537 0.5610.4590.444 0.4950.464 0.5850.516 0.481 0.4560.4080.410 0.4350.428 0.4990.462 0.4290.4250.4000.407 0.4380.438 0.527 0.502 0.435 0.4370.7950.669 1.212 0.871 1.1660.823 0.961 0.7340.658 0.592 0.8980.721 1.1020.8410.7990.671
LL96 192 336 7200.173 0.262 0.229 0.301 0.2860.341 0.3780.40110.192 0.245 0.302 0.3990.281 0.317 0.352 0.4080.167 0.269 0.2240.303 0.2810.342 0.3970.4210.1650.255 0.220 0.292 0.2740.329 0.362 0.385[0.187 0.267 0.2490.309 0.321 0.351 0.4080.4030.421（[0.203 0.287 0.269 0.328 0.3250.366 0.4150.2550.339 0.281 0.340 0.3390.372 0.4330.4320.1920.274 0.2800.339 0.3340.361 0.4170.4130.189 0.280 0.2530.319 0.3140.357 0.4140.413[0.209 0.308 0.311 0.382 0.4420.466 0.675 0.587|0.3650.453 0.5330.563 1.3630.8871.078 0.8270.658 0.619 1.5490.972
æ—¥Avg 24 36 480.2660.326 2.0630.881 1.8680.892 1.7900.8840.284 2.723 2.027 2.2060.339 1.099 0.966 1.0220.2670.333 2.215 1.081 1.9630.963 2.1301.0240.2550.315 1.3190.754 1.4300.834 1.5530.8150.291 2.317 1.9720.333 0.934 0.920 2.2380.9403.228 2.679 2.6220.3050.349 1.260 1.080 1.0780.327 3.483 3.1030.371 1.287 2.294 1.148 1.8250.3060.347 0.945 0.8480.2930.342 2.527 1.020 2.615 1.0070.4090.436 8.313 2.144 6.631 1.9023.3791.338 1.410 0.810 5.764 1.677 4.755 1.4672.631 1.242 1.4790.915 4.4001.3824.7831.448
60 Avg 96 1921.979 0.957 1.925 0.903 0.1390.238 0.1530.2511.976 2.233 0.138 0.1520.983 1.017 0.234 0.2472.368 1.096 2.169 1.041 [0.1400.237 0.153 0.2491.470 0.788 1.4430.797 0.129 0.222 0.1570.2402.0270.928 2.1390.931 0.1680.272 0.1840.2892.857 2.847 10.193（ 0.201（1.157 1.144 0.308 0.3152.669 2.770 3.006 0.2011.085 1.125 2.178 1.161 2.077 0.3172.010 0.900 0.963 0.914 0.1690.2732.359 0.972 2.487 1.016 2.497 1.004 [0.187 0.3047.299 1.982 7.283 1.985 7.382 2.003 10.207 0.3074.763 5.264 5.137 |0.2740.3681.469 1.564 1.5444.832 1.465 4.8821.483 4.7241.445 [0.312 0.402
GCE336 720 Avg0.169 0.266 0.2060.2970.1680.2630.169 0.2670.1630.2590.1980.3000.2140.3290.2220.334 0.1820.2860.1990.3150.213 0.3160.2960.386 0.3000.3940.3480.433
0.4120.2940.632
Average Avg0.4140.294 [0.516 0.4070.628 0.3790.573004310.5620.436044606596043307010.4890570.510.634650620473.300668360750.6240.3400.621 0.3960.622 0.3920.8640.472 0.764 0.4160.7420.420 0.7550.423 0.741 0.422
336 7200.4500.3120.413 0.447 0.4130.2810.4330.2950.390 0.2630.6400.350 0.620 0.3360.383 0.6260.382 0.610 0.3760.6160.382 0.6220.337 0.6600.4080.6530.3550.3960.6130.386 0.658 30.4070.719 0.391 0.6960.379 0.7770.4200.732 0.423 0.7330.420
96 1920.254
0.1670.2630.2070.2950.2030.3010.197 0.2900.2200.3200.2460.3550.2310.3380.2000.3040.2120.3290.2300.3330.350 0.433
0.3880.2820.1660.2590.166 0.2630.161 0.2520.1920.295 0.5930.3210.2140.3270.361 0.222 0.338 0.1930.321 0.2960.2330.3450.265 0.360 0.229 0.3290.373 0.439 0.3110.3970.3400.420 0.338 0.422
0.2270.2080.323
mffors0.4070.2900.3900.2720.410 0.282 0.4230.287 0.4360.2960.360 0.2490.617 0.336 0.6290.3360.615 0.391 0.382
0.4030.276 0.280 0.2980.4660.3150.379 0.256 0.3920.264 0.4320.2860.587 0.366 0.6040.373 0.621（0.613 0.3880.612 0.338 0.6130.340 0.6180.3280.607 0.392 0.621 0.399 0.6220.3960.601
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Methods MetricGPT2(6)5% MSE MAEGPT2(6)10% MSE MAEETS MSE MAEARIMA MSE MAENaiveDrift MSE MAE
LL96 1920.376 0.4180.421 0.4410.331 0.4020.374 0.4112.954 10.2260.742 1.2120.481 0.5850.443 0.4950.764 1.5600.561 0.785
[uLL96 1920.386 0.4400.405 0.4380.390 0.4290.404 0.42352.237 186.4452.689 4.6540.693 0.7100.547 0.5571.539 2.8690.913 1.215
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Methods MetricGPT2(6)PatchTSTDLinearAutoformerAutoformer(Revin)FEDformerFEDformer(Revin)
MSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
L960.1990.2800.2060.2880.2360.3260.2320.3220.2240.3000.2290.3200.2230.298
1920.2560.3160.2640.3240.3060.3730.2910.3570.2960.3430.2940.3610.2880.336
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Methods MetricGPT2-backbone(6Layers) MSE MAE
LLE96 192 336 7200.376 ± 0.0072 0.418 ± 0.0013 0.408 ± 0.00060.421 ± 0.0054 0.441 ± 0.0014 0.439 ± 0.0002
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MetricMSEMAEMSEMAEMSEMAE
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960.3760.4210.4400.4490.4650.457
1920.4180.4410.5030.4780.6140.536
LLa3360.4080.4390.6910.5720.5960.529
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960.1990.2800.2170.2930.3010.353
LL1920.2560.3160.3000.3500.3210.365
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MetricMSEMAEMSEMAEMSEMAE
weeeet960.1630.2150.1680.2210.1750.229
1920.2100.2540.2380.2860.2440.287
3360.2560.2920.2890.3180.3010.325
7200.3210.3390.3980.3830.3900.378
LLE960.4580.4560.6050.5320.6800.560
1920.5700.5160.7130.5790.7380.602
3360.6080.5350.7470.5860.8930.641
7200.7250.5910.9450.6882.9941.169
960.3310.3740.3690.3940.4220.433
LLa1920.4020.4110.4640.4550.4820.466
3360.4060.4330.4200.4390.5400.496
7200.4490.4640.5350.5150.5640.519
LL960.3900.4040.4290.4300.3850.401
1920.4290.4230.4630.4460.4260.421
3360.4690.4390.5100.4700.5060.455
7200.5690.4980.7800.5910.5760.505
LLa960.1880.2690.2430.3110.2440.315
1920.2510.3090.3070.3520.3180.363
3360.3070.3460.3370.3640.4090.412
7200.4260.4170.4710.4400.4730.450
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MethodsGPT2(6)No FreezeNo PretrainNo Pretrain + Freeze
MetricMSEMAEMSEMAEMSEMAEMSEMAE
LLa960.3760.4210.4400.4490.4650.4570.5400.497
1920.4180.4410.5030.4780.6140.5360.7210.580
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MethodsClassical methods XGBoost RocketRNNTCNTrans. Re.MLP DLinear LightTS.TimesNetGPT2(6)
LSTNet LSSLIn.Pyra.Auto. Station.FED.ETS. Flow.29.7
EthanolConcentration43.745.239.931.128.932.731.931.630.831.632.731.228.133.832.635.734.2
FaceDetection63.364.765.766.752.867.368.667.065.768.468.066.066.367.668.067.568.669.2
Handwriting15.858.825.824.653.332.027.432.829.436.731.628.032.533.827.026.132.132.7
Heartbeat73.275.677.172.775.676.177.180.575.674.673.773.771.277.675.175.178.077.2
JapaneseVowels86.596.298.198.498.998.797.898.998.496.299.298.495.998.996.296.298.498.6
PEMS-SF98.375.186.786.168.882.182.781.583.282.787.380.9 86.083.875.188.489.687.9
SelfRegulationSCP184.690.884.090.884.692.290.490.188.184.089.488.789.692.587.389.891.893.2
SelfRegulationSCP2 SpokenArabicDigits48.953.352.852.255.653.956.753.353.350.657.254.4 55.056.150.551.157.259.4
UWaveGestureLibrary69.6 75.971.2 94.4100.0 87.8100.095.698.4 85.697.0100.099.6100.0100.0100.0 100.098.881.4 82.1100.0 80.399.0 85.399.2 88.1
Average72.571.885.9 70.988.4 70.371.985.6 71.585.6 72.183.4 70.885.9 71.187.5 72.785.3 70.785.0 71.086.6 73.067.570.473.6
66.074.0
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MethodsMetricETTh2ETTm2
9619233672096192336720
GPT2-backbone(6 Layers)MSE0.3760.421 0.408-0.1990.2560.3180.460
MAE0.4190.441 0.439-0.2800.3160.3530.436
BERT-backbond(6 Layers)MSE MAE0.397 0.4180.480 0.4650.481 0.472- =0.222 0.3000.281 0.3350.331 0.3670.441 0.428
BEiT-backbond(6 Layers)MSE MAE|0.405 0.4180.448 0.446 0.5000.5240.208 0.2910.272 0.3260.3310.452
DLinearZeng et al. (2023)MSE MAE0.4420.617 0.4560.5421.424- -0.2360.3060.362 0.3800.433 0.674
PatchTSTNie et al. (2022)MSE MAE[0.401 0.4210.452 0.4550.4690.849 0.464- -0.3260.373 [0.2060.2640.423 0.3340.583 0.454
FEDformerZhou et al. (2022)MSE MAE0.390 0.4240.457 0.4650.4830.477- -0.2880.324 0.2990.290 0.378 0.5230.3670.483
AutoformerWu et al. (2021)MSE MAE0.428 0.496 0.486 0.468 0.504 0.496- -0.320 0.361 [0.232 0.291 0.3220.3570.427 0.478 0.5170.510 0.533 0.538
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MethodsMask RatioGPT2(3)MSE MAETimesNetMSE MAEPatchTSTMSE MAEETSformerMSEMAELightTSMSE MAEDLinearMSE MAEFEDformerMSE MAEStationaryMSEMAEAutoformerMSE MAEInformerMSE MAEReformer|MSE MAE
12.5%[L] 25%37.5%50%Avg0.017 0.0850.022 0.0960.0290.1110.040 0.1280.0280.1050.0230.1010.0230.1010.0290.1110.036 0.1240.0270.1070.0410.1300.0440.1350.0490.1430.055 0.1510.0470.1400.0960.2290.0960.2290.1330.2710.1860.3230.1200.2530.0930.2060.0930.2060.1130.2310.1340.2550.104 0.2180.0800.1930.080 0.1930.1030.2190.132 0.2480.0930.2060.0520.1660.0520.1660.069 0.1910.089 0.2180.062 0.17710.0320.1190.0320.1190.0390.1310.0470.1450.0360.126[0.0460.144|0.0460.1440.0570.1610.0670.1740.0510.1500.0630.180|0.0630.1800.0790.2000.093 0.2180.0710.188[0.042 0.1460.0420.1460.0630.1820.082 0.2080.0550.166
12.5%L 25%0.0170.0760.0200.0800.0220.0870.0180.0800.0200.0850.0230.09110.0260.0940.0280.0990.030 0.1040.0340.1100.0290.1020.1080.2390.1640.2940.2370.3560.3230.4210.2080.32710.0340.1270.042 0.1430.0510.1590.062 0.1660.0850.1960.1060.2220.131 0.2470.0960.2080.0560.1590.080 0.1950.110 0.2310.156 0.2760.1010.2150.0210.0880.0240.0960.0270.1030.0300.1080.0260.0990.0230.0920.0260.1010.0300.1080.1330.2700.1350.2720.1550.2930.108 0.2280.1360.2620.1750.3000.211 0.3290.1570.280
L 37.5%50%Avg0.0220.087
0.0250.0950.0210.0840.0260.0980.0220.0880.0590.1740.046 0.1510.0350.1190.0290.1050.2000.3330.1560.292
12.5%LLT 25%37.5%0.0430.1400.054 0.1560.0570.1590.069 0.1780.0930.2010.107 0.2170.120 0.2300.1260.2630.169 0.3040.220 0.3470.240 0.3450.265 0.3640.151 0.2670.180 0.29210.0700.1900.106 0.23610.0600.1650.080 0.1890.102 0.2120.074 0.1820.0900.2030.109 0.2220.1140.2340.140 0.2620.1740.29310.0740.1940.1020.2270.135 0.2610.179 0.2980.122 0.245
0.0720.084
50%0.1070.1020.2150.1410.248
0.1730.187
0.2020.4020.3290.3340.4040.2840.3730.2010.3060.1170.2460.0940.2010.0940.2010.1370.2480.1030.2140.215 0.3250.1610.2790.122 0.245
Avg0.0691730.0780.1150.224
12.5%LLE 25%37.5%0.0390.044
44
0.1250.1350.0400.0460.1300.1410.0570.1520.0610.15810.1870.3190.2790.3900.1010.2310.1150.2460.1000.1270.2160.24710.0950.2120.1370.2580.0420.0490.1470.1330.0490.1470.0440.1380.050 0.1490.3050.4310.3220.4440.163 0.2890.206 0.3310.2520.3700.316 0.4190.2340.352
0.0510.147
50%Avg0.0590.0.0600.1620.0730.1740.6020.5720.3670.4360.136 0.2680.1190.2500.1830.2990.1420.2590.2990.2320.3410.0650.1700.0680.1730.3690.472472
0.0480.1410.0490.1460.0650.1630.1630.2790.05330.1520.0550.1560.3370.452
12.5%GEE 25%37.5%50%Avg0.080 0.1940.0870.0940.080 0.1940.2030.2110.0850.2020.089）0.2060.0940.21310.055 0.16010.1960.3210.2070.3320.102 0.2290.1210.2520.0920.2140.118 0.2470.1070.23710.0930.2100.0970.2140.089 0.2100.0960.2200.218 0.32610.1900.3080.197 0.312
0.0650.1750.0760.1890.2190.219 0.326
0.1010.0900.2200.2070.1000.0920.2210.0910.2080.2350.357570.1600.2930.1310.2620.1750.3050.1320.2600.1580.2840.1080.2280.2280.1130.2390.2280.3310.2220.328
0.2030.3150.210 0.3190.2000.313
0.0920.2100.0720.1830.2140.3390.130 0.2590.100 0.2180.1010.225
12.5%wrees 25%37.5%50%Avg0.0260.040490.0250.0450.0290.0520.0290.0490.0570.141[0.0470.1010.052 0.111[0.0390.084|0.0480.1030.041 0.1070.0270.0510.0260.0470.0370.09310.031 0.076
0.0280.00.0310.0530.0650.155
0.0400.091
0.0370.0650.0310.0560.0380.0630.1020.2070.0650.1330.0660.1340.1830.3120.0370.0680.0370.0670.053 0.114
0.0300.0540.0600.144
0.0460.0990.0380.087
0.0760.1710.0550.1170.052 0.1100.0990.2030.0320.0590.0310.0570.0450.104
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Methods MetricsPSMD RPMSLF1SMAP RPSWaTF1PSM RF1AvgF1 %
F1RPF1R
GPT(6)88.8984.9886.8982.0082.9182.4590.6060.9572.8892.2096.3494.2398.6295.68 97.1386.72
TimesNet*87.9181.5484.6189.5475.3681.8490.1456.4069.3990.7595.4093.0298.5196.2097.3485.24
PatchTST87.2682.1484.6288.3470.9678.7090.6455.4668.8291.1080.9485.7298.8493.4796.0882.79
ETSformer87.4479.2383.1385.1384.9385.0392.2555.7569.5090.0280.3684.9199.3185.2891.7682.87
FEDformer87.9582.3985.0877.1480.0778.5790.4758.1070.7690.1796.4293.1997.3197.1697.2384.97
LightTS87.1078.4282.5382.4075.7878.9592.5855.2769.2191.9894.7293.3398.3795.9797.1584.23
DLinear83.6271.5277.1084.3485.4284.8892.3255.4169.2680.9195.3087.5298.2889.2693.5582.46
Stationary88.3381.2184.6268.5589.1477.5089.3759.0271.0968.0396.7579.8897.8296.7697.2982.08
Autoformer88.0682.3585.1177.2780.9279.0590.4058.6271.1289.8595.8192.7499.0888.1593.2984.26
Pyraformer85.6180.6183.0483.8185.9384.8692.5457.7171.0987.9296.0091.7871.6796.0282.0882.57
Anomaly Transformer"*88.9182.2385.4979.6187.3783.3191.8558.1171.1872.5197.3283.1068.3594.7279.4080.50
Informer86.6077.2381.6581.7786.4884.0690.1157.1369.9270.2996.7581.4364.2796.3377.1078.83
Reformer82.5869.2475.3285.5183.3184.4090.9157.4470.4072.50 96.5382.8059.9395.3873.6177.31
LogTransformer83.4670.1376.2173.0587.3779.5789.1557.5969.9768.67 97.3280.5263.0698.0076.7476.60
Transformer83.5876.1379.5671.5787.3778.6889.3757.1269.7068.84 96.5380.3762.7596.5676.0776.88
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MethodsGPT2(6）TimesNetPatchTSTN-HiTSN-BEATSETSformerLightTSDLinear FEDformer Stationary Autoformer Informer Reformer
SMAPE13.53113.38713.47713.41813.43618.00914.24716.96513.72813.71713.97414.72716.169
heeaMASE3.0152.9963.0193.0453.0434.4873.1094.2833.0483.0783.1343.4183.800
OWA0.7930.7860.7920.7930.7941.1150.8271.0580.8030.8070.8220.8810.973
tttniSMAPE10.17710.10010.3810.20210.12413.37611.36412.14510.79210.95811.33811.36013.313
MASE1.1941.1821.2331.1941.1691.9061.3281.5201.2831.3251.3651.4011.775
OWA0.8980.8900.9210.8990.8861.3021.0001.1060.9580.9811.0121.0271.252
SMAPE12.89412.67012.95912.79112.67714.58814.01413.51414.26013.91713.95814.06220.128
nnyauoMASE0.9560.9330.9700.9690.9371.3681.0531.0371.1021.0971.1031.1412.614
OWA0.8970.8780.9050.8990.8801.1490.9810.9561.0120.9981.0021.0241.927
SMAPE4.9404.8914.9525.0614.9257.26715.8806.7094.9546.3025.48524.46032.491
DirttMASE3.2283.3023.3473.2163.3915.24011.4344.9533.2644.0643.86520.96033.355
OWA1.0291.0351.0491.0401.0531.5913.4741.4871.0361.3041.1875.8798.679
SMAPE11.99111.82912.05911.92711.85114.71813.52513.63912.84012.78012.90914.08618.200
aaeeeeeMASE1.6001.5851.6231.6131.5992.4082.1112.0951.7011.7561.7712.7184.223
OWA0.8610.8510.8690.8610.8551.1721.0511.0510.9180.9300.9391.2301.775
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