Leaderboards

Leaderboard for univariate time series forecasting

Learning Paradigm  [all]


Metrics  [all]


Frequency

Characteristics


Score

Rank Model Score 🥇 🥈 🥉 Paper Publication Year
1 Linear Regression 5911 2570 1902 1439 paper Wiley [bib] 2005
2 TimesNet 5683 1945 1908 1830 paper ICLR [bib] 2023
3 N-HiTS 4761 1997 1452 1312 paper AAAI [bib] 2023
4 Random Forest 4403 1522 1503 1378 paper ML [bib] 2021
5 N-BEATS 4168 1510 1411 1247 paper ICLR [bib] 2020
6 Arima 3935 1403 1282 1250 paper JASA [bib] 1970
7 Xgboost 3776 1320 1209 1247 paper KDD [bib] 2016
8 PatchTST 3477 969 1148 1360 paper ICLR [bib] 2023
9 Naive Drift 3383 1032 995 1356 paper Darts [bib] ——
10 Naive Moving Average 3149 1000 1143 1006 paper Darts [bib] ——
11 TiDE 3046 963 1031 1052 paper arXiv [bib] 2023
12 Informer 3003 968 982 1053 paper AAAI [bib] 2021
13 FEDformer 2414 715 771 928 paper ICML [bib] 2022
14 FiLM 2300 753 764 783 paper NeurIPS [bib] 2022
15 Naive Seasonal 2143 0 1000 1143 paper Darts [bib] ——
16 Non-stationary Transformers 2091 607 733 751 paper NeurIPS [bib] 2022
17 AutoCES 2056 679 669 708 paper Darts [bib] ——
18 Kalman Filter 1907 809 569 529 paper CUP [bib] 1990
19 AutoTheta 1846 454 682 710 paper Darts [bib] ——
20 AutoETS 1791 467 567 757 paper Darts [bib] ——
21 LightGBM 1564 553 560 451 paper NIPS [bib] 2017
22 Naive Mean 1506 531 524 451 paper Darts [bib] ——
23 DLinear 1155 232 383 540 paper AAAI [bib] 2023
24 NLinear 1089 430 336 323 paper AAAI [bib] 2023
25 Triformer 654 230 249 175 paper IJCAI [bib] 2022
26 RNN 603 238 178 187 paper arXiv [bib] 2019
27 Crossformer 396 127 129 140 paper ICLR [bib] 2023
28 TCN 387 175 119 93 paper arXiv [bib] 2018

Rules:

  • For univariate forecasting algorithms, we consider 8,068 series, and the MAE、MSE、MSMAPE metrics, thus having 24,204 (8,068 * 3) unique evaluation settings, click here to see the detailed results, click here to download detailed evaluation results for each of the 8,068 univariate time series.
  • Datasets are classified by sampling frequency into Yearly, Quarterly, Monthly, Weekly, Daily, Hourly, and Other. Their corresponding forecasting horizons are 6, 8, 18, 13, 14, 48, and 8, respectively. The look-back window is set to 1.25 times the respective forecasting horizon.
  • For each forecasting algorithm, we count the number of times that the algorithm receives the gold, silver, and bronze medals, i.e., having the lowest, 2nd lowest, and 3rd lowest errors, shown as 🥇, 🥈, and 🥉, respectively.
  • We provide three different types of scores for ranking the forecasting algorithms. First, the scores equal to the numbers of gold medals. Second, the scores are the sum of the numbers of gold, silver, and bronze medals. Third, the scores are the weighted sum of the gold, silver, and bronze medals, where the weights can be customized. The larger the score, the higher the ranking.

Univariate forecasting results

Results classified according to characteristics

DatasetsMetricCrossformerN-HiTSTiDEDLinearNLinearPatchTSTTimesNetFEDformerFiLMStationaryTriformerRFInformerN-BEATSRNNTCNLightGBMXgboostLRKFArimaNDNMNMANSAutoCESAutoETSAutoTheta

Seasonality

mase29.7042.1892.0742.4092.8501.6601.4462.1001.8822.38419.378

1.649

2.3902.08129.45624.1593.4261.7157.9e+99.0022.8304.1118.8554.1644.1642.8454.0913.901
msmape161.07413.55714.56619.62820.938

12.263

10.92719.04113.53715.190107.95712.79014.30115.794155.612121.33518.26313.40419.18357.40919.86823.68645.38621.60621.60619.22726.38627.179
mase_rank172011752231129

329

511413312235601471917592125881442037225470633051
msmape_rank171961561932147

303

511342911259611541815572265971442067628440583346
×mase23.7041.6782.5261.9491.7331.6391.4781.8791.7691.63816.4961.7311.6011.67723.25715.4413.2671.8142.6e+103.318

1.496

1.5949.1911.6501.6501.6451.5441.503
msmape166.85924.12730.96826.96627.15421.67120.49726.76622.33122.050138.94525.316

21.413

25.705160.553140.17435.61426.83833.41344.55124.49125.96145.34022.75322.75321.80525.19025.697
mase_rank234741395110718932119210916660272261

367

7142126222244147231279153317016612398
msmape_rank244771505310819231818811016456275252

345

69441232222501492322831483290160125105

Trend

mase41.2872.5533.3163.0162.914

2.220

1.9112.7582.4922.65128.0912.2712.6582.51240.78828.7164.8742.3557.9e+98.4862.8223.61115.6863.7893.7892.8173.6153.486
msmape184.12511.09013.74714.43513.463

10.679

9.24713.91711.44211.709133.42410.83211.21611.583181.222136.24324.34811.22116.92050.06211.68614.27543.44013.19113.19111.95712.98614.322
mase_rank23371804972158

393

1031599622217150255688518968880295158771040154106115
msmape_rank23411804878177

376

103153951921914524846851947038029716175960146112116
×mase8.9411.1161.2721.1311.326

1.007

0.9681.0771.0521.1275.8781.0591.0641.0738.7117.7181.1271.1273.1e+102.1851.1041.3971.6481.3141.3141.1971.3111.246
msmape142.82430.05336.80234.97237.374

26.261

25.24334.80827.30727.894119.76031.26226.99333.385133.399129.15334.69333.30740.21048.91135.01937.16647.50332.50732.50731.52839.81439.629
mase_rank3833813424661602571409110350

290

17125984511002451442111391931012600754734
msmape_rank393321262462162245136919848

315

1682518353952541442131411981012770724635

Stationarity

mase9.3801.2121.3431.1391.290

1.004

0.9611.0571.0661.1326.3091.0431.1331.1629.2167.8701.1871.10015.8483.1721.2571.6771.9711.5941.5941.1891.6181.544
msmape135.88831.08037.59435.43437.306

27.024

26.12035.12228.17228.539114.32332.23227.54633.519128.366122.19431.22934.28138.32052.23436.21238.61548.13933.87633.87631.21641.51340.645
mase_rank342531061958130220119798356

224

143202805097196146197125127772200583738
msmape_rank37

240

1011955134206114798251258141194825093198150197122132782310534037
×mase36.8262.3053.0072.7682.732

2.065

1.7932.5532.2972.45124.9452.1252.4082.26936.32025.9074.4312.2143.1e+107.0322.5003.14313.6643.2883.2882.5853.1183.003
msmape183.26412.88516.22516.80016.610

12.206

10.75416.42512.94013.397135.17712.85312.90414.325178.281139.83627.26913.45521.16847.75713.94216.30643.55414.80914.80914.98115.36516.947
mase_rank64222085480188

430

1241711161628317831210988238686943092241011440171116111
msmape_rank4

433

205538520541512516511116276172305598725069796316227981420165118114

Transition

mase19.7591.6011.8271.8201.9851.3971.2821.5711.5051.74411.972

1.380

1.7791.54319.41413.7442.0981.4745.7e+43.9981.9302.7395.8912.6842.6841.9492.7232.603
msmape155.70022.67227.66425.74129.013

21.932

20.86924.80322.97323.707117.24023.00222.97823.031151.088125.13626.48624.54529.17945.52125.02030.83336.61028.37628.37625.50428.72529.234
mase_rank35

457

2103783214440168164132654202243488756137334481852301761542400977152
msmape_rank36

451

1983680222422165159130604482203418457135346489872261811522510947453
×mase37.3722.3713.3032.6822.489

2.102

1.7992.6762.3692.27727.8312.2782.1362.35836.96127.9874.9842.3235.3e+108.2592.1572.25314.8102.5062.5062.2842.1722.113
msmape180.77515.28419.14321.21617.03910.9849.43521.93211.62211.399144.59115.905

10.860

19.785172.323146.94231.45416.40425.62956.75418.52014.67361.19411.32911.32913.55420.08920.905
mase_rank5

218

10436551042107586677879716633481003512062041752412401328297
msmape_rank5

222

10836601171997485637869315832451023582062121782412201248498

Shifting

mase36.0922.3452.9752.8232.747

2.138

1.8572.6462.3522.50725.5702.2242.3142.28935.61224.9254.8352.3063.7e+106.8622.3312.83614.6103.0023.0022.6952.7992.676
msmape173.92414.24817.86019.93019.013

13.453

11.87319.87414.07414.454133.55414.87713.50916.573168.690137.11328.25216.15921.77550.84417.55018.60852.31016.20916.20915.32920.51721.668
mase_rank103431534380150

373

1051367923176169248211358168530214284168491360148110106
msmape_rank103491534384168

354

991337725185164240201057171536213294173461320140114107
×mase15.6391.3901.7091.4101.563

1.142

1.0621.2621.2571.3559.4011.1591.4851.36315.38112.4991.3941.2297.4e+44.1221.6812.2883.3412.2282.2281.4112.2482.174
msmape155.03126.02231.61828.46530.674

22.763

21.88127.81123.94524.258120.18326.25423.98327.347148.280128.54429.07327.31034.25148.15028.02231.76238.18628.60528.60526.88230.95031.018
mase_rank30332161305816827713811412049

331

1522666946127266302771501831292280814343
msmape_rank31

324

1532956171267140111116423491492596749123277311801441861302410784444

Results classified according to frequency

DatasetsMetricCrossformerN-HiTSTiDEDLinearNLinearPatchTSTTimesNetFEDformerFiLMStationaryTriformerRFInformerN-BEATSRNNTCNLightGBMXgboostLRKFArimaNDNMNMANSAutoCESAutoETSAutoTheta
Hourly
mase9.6701.4941.2191.4571.8651.2390.9521.1651.3551.8846.850

0.884

3.0871.1159.3849.631NaN0.9860.8687.9544.3167.1587.3227.2447.244NaN7.4927.160
msmape73.12424.46931.18127.31929.86025.53023.85928.48028.33730.70236.42124.27429.396

24.061

70.49241.590NaN28.92128.47370.38236.71350.21643.16549.58049.580NaN48.71449.235
mase_rank6552151419

101

23284187919271314060145131423200030
msmape_rank8531351123911727316

102

1726159065149151412210030
Daily
mase19.9450.9961.1731.2751.2471.079

1.024

1.1741.1101.14310.5201.1591.0981.06519.4447.917NaN1.2371.3431.2061.1091.2545.9181.2251.2251.2621.2101.167
msmape120.25623.46426.19726.79224.89520.66219.54725.422

20.507

22.20571.53225.38821.10723.516112.61377.606NaN25.92326.46322.00425.98424.51342.84323.78723.78724.45725.82624.652
mase_rank2818161121716816924493813173

144

564001167532373715111021811
msmape_rank3017563131714786821483513275

143

57460128763031361511801889
Weekly
mase44.1391.3001.7581.8031.5471.2961.1821.3451.4301.28522.4041.588

1.207

1.42643.8597.6492.6701.72132.4541.3701.4981.71023.5881.5551.5551.4281.5151.615
msmape144.66132.19639.46150.16440.25517.95717.13753.29317.81118.27075.39235.27617.44353.560106.53471.95951.59336.48256.27919.28843.37137.112113.55914.490

14.490

30.52549.86963.426
mase_rank337161241943111520530233017015213315351

111

599010135
msmape_rank137181131643101819529232713013223115355

119

5107010116
Monthly
mase29.5471.5251.3881.7642.280

1.117

1.0531.3921.3101.86713.7251.1481.5411.48629.42720.2781.6701.2365.5e+92.1201.7252.6165.3522.5452.5452.3392.5772.342
msmape193.17714.90417.17216.28521.481

13.718

13.40214.67815.14816.378118.47513.95515.25014.698192.250137.98116.49114.90317.21418.35516.22622.25228.82021.00121.00118.75020.19118.223
mase_rank095821111121

222

47913031406574105410027832722329300302013
msmape_rank097791011132

212

5390294136647110549928431692327350292014
Quarterly
mase19.2011.4161.4381.9022.2171.1871.1271.7411.4181.72918.3621.4011.3951.44119.19420.2632.6621.4331.2111.903

1.164

1.9405.7221.9841.9841.7771.7261.706
msmape198.23815.64818.29518.07023.06714.42513.99116.81315.99416.753191.48915.48215.10315.031198.359192.93921.73316.34816.00019.524

14.235

18.58335.98818.24118.24117.44017.25116.572
mase_rank010472102587127375247267678600576719324

140

5270330373820
msmape_rank010377102496120375048165628300606819427

140

5069310364122
Yearly
mase24.3873.8706.2773.8113.1143.4762.9213.8913.4703.29724.2933.2083.3443.74524.36329.2246.2833.2519.5e+1019.0123.242

2.783

7.2763.0393.0393.1682.8642.729
msmape198.21120.77630.44623.54022.01822.23718.99023.86422.11820.281199.30720.60221.38620.247197.946199.59936.93921.33341.919157.05120.26820.11242.55419.93519.93520.27219.464

19.314

mase_rank0175391155445940323603960

127

105953722091111496101175990
msmape_rank0181371161476038313304158

121

0053497720100113525101116590
Other
mase59.5412.7092.6943.2123.1232.307

2.153

3.6173.4342.63442.5443.1982.2892.55755.49248.087NaN3.3582.3782.5962.0932.38030.3452.9412.9412.3702.2322.358
msmape157.85810.10210.28313.84113.91610.952

9.853

13.80413.57612.069115.99011.15110.3909.770151.264122.739NaN12.20612.01515.01312.09713.25836.15213.90513.90511.65712.94412.935
mase_rank3282312121217168136211426250173617

29

157100141210
msmape_rank2271912131117167136291428140173617

29

176100141010