tables/pairwise_MASE.csv

model_1,model_2,win_rate,win_rate_lower,win_rate_upper,skill_score,skill_score_lower,skill_score_upper
Chronos-2,Chronos-2,0.5,0.5,0.5,0.0,0.0,0.0
Chronos-2,TiRex,0.72,0.63,0.81,0.078,0.052,0.108
Chronos-2,TimesFM-2.5,0.71,0.62,0.79,0.076,0.048,0.103
Chronos-2,Toto-1.0,0.74,0.65,0.83,0.101,0.073,0.133
Chronos-2,Moirai-2.0,0.92,0.86,0.97,0.113,0.086,0.141
Chronos-2,Chronos-Bolt,0.94,0.89,0.98,0.122,0.096,0.15
Chronos-2,TabPFN-TS,0.85,0.77,0.92,0.108,0.08,0.14
Chronos-2,Sundial-Base,0.91,0.85,0.96,0.143,0.113,0.172
Chronos-2,Stat. Ensemble,0.86,0.79,0.93,0.235,0.19,0.277
Chronos-2,AutoARIMA,0.95,0.9,0.99,0.273,0.23,0.315
Chronos-2,AutoTheta,0.94,0.89,0.98,0.275,0.236,0.316
Chronos-2,AutoETS,0.89,0.83,0.95,0.34,0.28,0.401
Chronos-2,Seasonal Naive,0.98,0.95,1.0,0.355,0.318,0.393
Chronos-2,Naive,0.98,0.95,1.0,0.447,0.388,0.505
Chronos-2,Drift,0.94,0.89,0.98,0.454,0.392,0.513
TiRex,Chronos-2,0.28,0.19,0.37,-0.085,-0.121,-0.055
TiRex,TiRex,0.5,0.5,0.5,0.0,0.0,0.0
TiRex,TimesFM-2.5,0.485,0.385,0.585,-0.003,-0.019,0.014
TiRex,Toto-1.0,0.615,0.52,0.71,0.025,0.003,0.046
TiRex,Moirai-2.0,0.765,0.685,0.845,0.038,0.021,0.055
TiRex,Chronos-Bolt,0.765,0.68,0.845,0.048,0.029,0.067
TiRex,TabPFN-TS,0.69,0.6,0.78,0.033,-0.01,0.074
TiRex,Sundial-Base,0.805,0.72,0.88,0.07,0.036,0.104
TiRex,Stat. Ensemble,0.81,0.73,0.89,0.17,0.132,0.21
TiRex,AutoARIMA,0.9,0.84,0.95,0.211,0.175,0.253
TiRex,AutoTheta,0.94,0.89,0.98,0.214,0.18,0.249
TiRex,AutoETS,0.84,0.77,0.91,0.284,0.225,0.345
TiRex,Seasonal Naive,0.97,0.94,1.0,0.3,0.264,0.339
TiRex,Naive,0.96,0.92,0.99,0.4,0.344,0.457
TiRex,Drift,0.94,0.89,0.98,0.408,0.347,0.462
TimesFM-2.5,Chronos-2,0.29,0.21,0.38,-0.082,-0.115,-0.05
TimesFM-2.5,TiRex,0.515,0.415,0.615,0.003,-0.014,0.019
TimesFM-2.5,TimesFM-2.5,0.5,0.5,0.5,0.0,0.0,0.0
TimesFM-2.5,Toto-1.0,0.57,0.485,0.66,0.028,0.005,0.051
TimesFM-2.5,Moirai-2.0,0.71,0.625,0.795,0.04,0.021,0.06
TimesFM-2.5,Chronos-Bolt,0.71,0.625,0.79,0.05,0.029,0.071
TimesFM-2.5,TabPFN-TS,0.67,0.58,0.77,0.035,-0.011,0.081
TimesFM-2.5,Sundial-Base,0.805,0.73,0.88,0.072,0.04,0.105
TimesFM-2.5,Stat. Ensemble,0.79,0.71,0.87,0.172,0.126,0.217
TimesFM-2.5,AutoARIMA,0.87,0.8,0.93,0.214,0.175,0.257
TimesFM-2.5,AutoTheta,0.9,0.83,0.95,0.216,0.177,0.255
TimesFM-2.5,AutoETS,0.84,0.76,0.91,0.286,0.228,0.347
TimesFM-2.5,Seasonal Naive,0.96,0.92,0.99,0.302,0.267,0.342
TimesFM-2.5,Naive,0.96,0.92,0.99,0.402,0.341,0.458
TimesFM-2.5,Drift,0.92,0.86,0.97,0.409,0.345,0.469
Toto-1.0,Chronos-2,0.26,0.17,0.35,-0.113,-0.154,-0.079
Toto-1.0,TiRex,0.385,0.29,0.48,-0.026,-0.048,-0.003
Toto-1.0,TimesFM-2.5,0.43,0.34,0.515,-0.028,-0.054,-0.005
Toto-1.0,Toto-1.0,0.5,0.5,0.5,0.0,0.0,0.0
Toto-1.0,Moirai-2.0,0.58,0.49,0.67,0.013,-0.008,0.034
Toto-1.0,Chronos-Bolt,0.56,0.46,0.645,0.023,-0.005,0.048
Toto-1.0,TabPFN-TS,0.58,0.49,0.67,0.008,-0.043,0.055
Toto-1.0,Sundial-Base,0.675,0.585,0.765,0.046,0.007,0.088
Toto-1.0,Stat. Ensemble,0.73,0.64,0.81,0.149,0.102,0.193
Toto-1.0,AutoARIMA,0.81,0.73,0.88,0.191,0.149,0.237
Toto-1.0,AutoTheta,0.82,0.74,0.89,0.194,0.151,0.235
Toto-1.0,AutoETS,0.79,0.71,0.86,0.266,0.203,0.326
Toto-1.0,Seasonal Naive,0.91,0.85,0.96,0.282,0.241,0.327
Toto-1.0,Naive,0.94,0.88,0.98,0.385,0.32,0.442
Toto-1.0,Drift,0.89,0.82,0.94,0.392,0.328,0.451
Moirai-2.0,Chronos-2,0.08,0.03,0.14,-0.128,-0.164,-0.094
Moirai-2.0,TiRex,0.235,0.155,0.315,-0.039,-0.059,-0.021
Moirai-2.0,TimesFM-2.5,0.29,0.205,0.375,-0.042,-0.064,-0.022
Moirai-2.0,Toto-1.0,0.42,0.33,0.51,-0.013,-0.036,0.008
Moirai-2.0,Moirai-2.0,0.5,0.5,0.5,0.0,0.0,0.0
Moirai-2.0,Chronos-Bolt,0.55,0.465,0.64,0.01,-0.012,0.032
Moirai-2.0,TabPFN-TS,0.52,0.43,0.62,-0.005,-0.054,0.038
Moirai-2.0,Sundial-Base,0.685,0.595,0.775,0.033,-0.004,0.067
Moirai-2.0,Stat. Ensemble,0.73,0.64,0.82,0.138,0.09,0.18
Moirai-2.0,AutoARIMA,0.81,0.73,0.88,0.18,0.138,0.228
Moirai-2.0,AutoTheta,0.85,0.77,0.91,0.183,0.144,0.223
Moirai-2.0,AutoETS,0.76,0.67,0.83,0.256,0.192,0.32
Moirai-2.0,Seasonal Naive,0.87,0.8,0.93,0.273,0.236,0.314
Moirai-2.0,Naive,0.91,0.85,0.96,0.377,0.316,0.433
Moirai-2.0,Drift,0.86,0.79,0.92,0.384,0.32,0.441
Chronos-Bolt,Chronos-2,0.06,0.02,0.11,-0.139,-0.177,-0.106
Chronos-Bolt,TiRex,0.235,0.155,0.32,-0.05,-0.072,-0.03
Chronos-Bolt,TimesFM-2.5,0.29,0.21,0.375,-0.053,-0.077,-0.03
Chronos-Bolt,Toto-1.0,0.44,0.355,0.54,-0.024,-0.051,0.005
Chronos-Bolt,Moirai-2.0,0.45,0.36,0.535,-0.01,-0.033,0.012
Chronos-Bolt,Chronos-Bolt,0.5,0.5,0.5,0.0,0.0,0.0
Chronos-Bolt,TabPFN-TS,0.52,0.42,0.61,-0.016,-0.062,0.025
Chronos-Bolt,Sundial-Base,0.605,0.51,0.695,0.024,-0.014,0.057
Chronos-Bolt,Stat. Ensemble,0.7,0.61,0.79,0.129,0.084,0.174
Chronos-Bolt,AutoARIMA,0.84,0.76,0.9,0.172,0.132,0.215
Chronos-Bolt,AutoTheta,0.86,0.79,0.92,0.174,0.137,0.212
Chronos-Bolt,AutoETS,0.77,0.68,0.85,0.248,0.184,0.315
Chronos-Bolt,Seasonal Naive,0.9,0.84,0.95,0.265,0.226,0.304
Chronos-Bolt,Naive,0.94,0.89,0.98,0.37,0.315,0.423
Chronos-Bolt,Drift,0.9,0.83,0.95,0.378,0.319,0.435
TabPFN-TS,Chronos-2,0.15,0.08,0.23,-0.122,-0.163,-0.087
TabPFN-TS,TiRex,0.31,0.22,0.4,-0.034,-0.08,0.01
TabPFN-TS,TimesFM-2.5,0.33,0.23,0.42,-0.036,-0.088,0.011
TabPFN-TS,Toto-1.0,0.42,0.33,0.51,-0.008,-0.058,0.041
TabPFN-TS,Moirai-2.0,0.48,0.38,0.57,0.005,-0.039,0.051
TabPFN-TS,Chronos-Bolt,0.48,0.39,0.58,0.015,-0.026,0.058
TabPFN-TS,TabPFN-TS,0.5,0.5,0.5,0.0,0.0,0.0
TabPFN-TS,Sundial-Base,0.53,0.43,0.63,0.039,-0.001,0.078
TabPFN-TS,Stat. Ensemble,0.645,0.545,0.735,0.142,0.089,0.19
TabPFN-TS,AutoARIMA,0.75,0.67,0.83,0.185,0.133,0.241
TabPFN-TS,AutoTheta,0.75,0.66,0.83,0.187,0.14,0.235
TabPFN-TS,AutoETS,0.72,0.63,0.81,0.26,0.183,0.332
TabPFN-TS,Seasonal Naive,0.91,0.855,0.96,0.276,0.231,0.321
TabPFN-TS,Naive,0.87,0.8,0.93,0.38,0.318,0.442
TabPFN-TS,Drift,0.87,0.8,0.94,0.388,0.321,0.45
Sundial-Base,Chronos-2,0.09,0.04,0.15,-0.167,-0.207,-0.128
Sundial-Base,TiRex,0.195,0.12,0.28,-0.075,-0.115,-0.037
Sundial-Base,TimesFM-2.5,0.195,0.12,0.27,-0.078,-0.117,-0.042
Sundial-Base,Toto-1.0,0.325,0.235,0.415,-0.048,-0.097,-0.007
Sundial-Base,Moirai-2.0,0.315,0.225,0.405,-0.035,-0.072,0.004
Sundial-Base,Chronos-Bolt,0.395,0.305,0.49,-0.024,-0.061,0.014
Sundial-Base,TabPFN-TS,0.47,0.37,0.57,-0.04,-0.085,0.001
Sundial-Base,Sundial-Base,0.5,0.5,0.5,0.0,0.0,0.0
Sundial-Base,Stat. Ensemble,0.66,0.56,0.76,0.108,0.051,0.16
Sundial-Base,AutoARIMA,0.76,0.67,0.84,0.152,0.098,0.203
Sundial-Base,AutoTheta,0.77,0.68,0.85,0.155,0.109,0.199
Sundial-Base,AutoETS,0.71,0.61,0.8,0.23,0.152,0.3
Sundial-Base,Seasonal Naive,0.88,0.81,0.94,0.247,0.206,0.288
Sundial-Base,Naive,0.88,0.8,0.94,0.355,0.289,0.417
Sundial-Base,Drift,0.83,0.75,0.9,0.363,0.291,0.428
Stat. Ensemble,Chronos-2,0.14,0.07,0.21,-0.308,-0.383,-0.234
Stat. Ensemble,TiRex,0.19,0.11,0.27,-0.205,-0.265,-0.152
Stat. Ensemble,TimesFM-2.5,0.21,0.13,0.29,-0.208,-0.277,-0.144
Stat. Ensemble,Toto-1.0,0.27,0.19,0.36,-0.175,-0.239,-0.113
Stat. Ensemble,Moirai-2.0,0.27,0.18,0.36,-0.16,-0.219,-0.099
Stat. Ensemble,Chronos-Bolt,0.3,0.21,0.39,-0.148,-0.211,-0.091
Stat. Ensemble,TabPFN-TS,0.355,0.265,0.455,-0.166,-0.235,-0.097
Stat. Ensemble,Sundial-Base,0.34,0.24,0.44,-0.121,-0.19,-0.054
Stat. Ensemble,Stat. Ensemble,0.5,0.5,0.5,0.0,0.0,0.0
Stat. Ensemble,AutoARIMA,0.64,0.545,0.73,0.05,0.02,0.09
Stat. Ensemble,AutoTheta,0.75,0.67,0.83,0.052,0.025,0.082
Stat. Ensemble,AutoETS,0.795,0.72,0.87,0.137,0.081,0.194
Stat. Ensemble,Seasonal Naive,0.795,0.725,0.865,0.157,0.116,0.203
Stat. Ensemble,Naive,0.85,0.78,0.92,0.277,0.218,0.346
Stat. Ensemble,Drift,0.89,0.82,0.95,0.286,0.225,0.35
AutoARIMA,Chronos-2,0.05,0.01,0.1,-0.376,-0.459,-0.298
AutoARIMA,TiRex,0.1,0.05,0.16,-0.268,-0.339,-0.212
AutoARIMA,TimesFM-2.5,0.13,0.07,0.2,-0.272,-0.346,-0.212
AutoARIMA,Toto-1.0,0.19,0.12,0.27,-0.236,-0.311,-0.175
AutoARIMA,Moirai-2.0,0.19,0.12,0.27,-0.22,-0.295,-0.16
AutoARIMA,Chronos-Bolt,0.16,0.1,0.24,-0.208,-0.274,-0.152
AutoARIMA,TabPFN-TS,0.25,0.17,0.33,-0.227,-0.317,-0.153
AutoARIMA,Sundial-Base,0.24,0.16,0.33,-0.179,-0.254,-0.108
AutoARIMA,Stat. Ensemble,0.36,0.27,0.455,-0.052,-0.099,-0.02
AutoARIMA,AutoARIMA,0.5,0.5,0.5,0.0,0.0,0.0
AutoARIMA,AutoTheta,0.55,0.45,0.64,0.003,-0.039,0.039
AutoARIMA,AutoETS,0.595,0.5,0.69,0.092,0.024,0.162
AutoARIMA,Seasonal Naive,0.75,0.665,0.83,0.112,0.068,0.161
AutoARIMA,Naive,0.77,0.69,0.85,0.239,0.169,0.312
AutoARIMA,Drift,0.8,0.72,0.87,0.249,0.174,0.324
AutoTheta,Chronos-2,0.06,0.02,0.11,-0.38,-0.462,-0.308
AutoTheta,TiRex,0.06,0.02,0.11,-0.272,-0.332,-0.22
AutoTheta,TimesFM-2.5,0.1,0.05,0.17,-0.275,-0.343,-0.215
AutoTheta,Toto-1.0,0.18,0.11,0.26,-0.24,-0.307,-0.178
AutoTheta,Moirai-2.0,0.15,0.09,0.23,-0.224,-0.287,-0.168
AutoTheta,Chronos-Bolt,0.14,0.08,0.21,-0.211,-0.269,-0.159
AutoTheta,TabPFN-TS,0.25,0.17,0.34,-0.23,-0.307,-0.163
AutoTheta,Sundial-Base,0.23,0.15,0.32,-0.183,-0.249,-0.122
AutoTheta,Stat. Ensemble,0.25,0.17,0.33,-0.055,-0.09,-0.025
AutoTheta,AutoARIMA,0.45,0.36,0.55,-0.003,-0.041,0.037
AutoTheta,AutoTheta,0.5,0.5,0.5,0.0,0.0,0.0
AutoTheta,AutoETS,0.59,0.5,0.69,0.089,0.026,0.155
AutoTheta,Seasonal Naive,0.78,0.7,0.86,0.11,0.069,0.149
AutoTheta,Naive,0.83,0.75,0.9,0.237,0.181,0.301
AutoTheta,Drift,0.82,0.74,0.9,0.247,0.189,0.31
AutoETS,Chronos-2,0.11,0.05,0.17,-0.515,-0.671,-0.39
AutoETS,TiRex,0.16,0.09,0.23,-0.397,-0.526,-0.291
AutoETS,TimesFM-2.5,0.16,0.09,0.24,-0.4,-0.531,-0.295
AutoETS,Toto-1.0,0.21,0.14,0.29,-0.362,-0.484,-0.254
AutoETS,Moirai-2.0,0.24,0.17,0.33,-0.344,-0.471,-0.237
AutoETS,Chronos-Bolt,0.23,0.15,0.32,-0.33,-0.459,-0.225
AutoETS,TabPFN-TS,0.28,0.19,0.37,-0.351,-0.498,-0.225
AutoETS,Sundial-Base,0.29,0.2,0.39,-0.299,-0.428,-0.179
AutoETS,Stat. Ensemble,0.205,0.13,0.28,-0.159,-0.241,-0.088
AutoETS,AutoARIMA,0.405,0.31,0.5,-0.101,-0.194,-0.024
AutoETS,AutoTheta,0.41,0.31,0.5,-0.098,-0.183,-0.027
AutoETS,AutoETS,0.5,0.5,0.5,0.0,0.0,0.0
AutoETS,Seasonal Naive,0.635,0.54,0.72,0.023,-0.071,0.103
AutoETS,Naive,0.64,0.55,0.73,0.162,0.086,0.251
AutoETS,Drift,0.68,0.59,0.77,0.173,0.098,0.258
Seasonal Naive,Chronos-2,0.02,0.0,0.05,-0.55,-0.648,-0.466
Seasonal Naive,TiRex,0.03,0.0,0.06,-0.429,-0.512,-0.359
Seasonal Naive,TimesFM-2.5,0.04,0.01,0.08,-0.433,-0.52,-0.365
Seasonal Naive,Toto-1.0,0.09,0.04,0.15,-0.393,-0.485,-0.318
Seasonal Naive,Moirai-2.0,0.13,0.07,0.2,-0.375,-0.458,-0.308
Seasonal Naive,Chronos-Bolt,0.1,0.05,0.16,-0.361,-0.437,-0.293
Seasonal Naive,TabPFN-TS,0.09,0.04,0.145,-0.382,-0.472,-0.301
Seasonal Naive,Sundial-Base,0.12,0.06,0.19,-0.329,-0.405,-0.259
Seasonal Naive,Stat. Ensemble,0.205,0.135,0.275,-0.186,-0.255,-0.131
Seasonal Naive,AutoARIMA,0.25,0.17,0.335,-0.127,-0.191,-0.073
Seasonal Naive,AutoTheta,0.22,0.14,0.3,-0.123,-0.176,-0.074
Seasonal Naive,AutoETS,0.365,0.28,0.46,-0.023,-0.115,0.067
Seasonal Naive,Seasonal Naive,0.5,0.5,0.5,0.0,0.0,0.0
Seasonal Naive,Naive,0.575,0.48,0.665,0.143,0.065,0.223
Seasonal Naive,Drift,0.7,0.6,0.79,0.154,0.067,0.238
Naive,Chronos-2,0.02,0.0,0.05,-0.809,-1.021,-0.634
Naive,TiRex,0.04,0.01,0.08,-0.667,-0.842,-0.525
Naive,TimesFM-2.5,0.04,0.01,0.08,-0.671,-0.844,-0.518
Naive,Toto-1.0,0.06,0.02,0.12,-0.625,-0.792,-0.471
Naive,Moirai-2.0,0.09,0.04,0.15,-0.604,-0.764,-0.463
Naive,Chronos-Bolt,0.06,0.02,0.11,-0.588,-0.733,-0.46
Naive,TabPFN-TS,0.13,0.07,0.2,-0.613,-0.791,-0.467
Naive,Sundial-Base,0.12,0.06,0.2,-0.55,-0.716,-0.407
Naive,Stat. Ensemble,0.15,0.08,0.22,-0.383,-0.529,-0.279
Naive,AutoARIMA,0.23,0.15,0.31,-0.314,-0.454,-0.204
Naive,AutoTheta,0.17,0.1,0.25,-0.311,-0.432,-0.222
Naive,AutoETS,0.36,0.27,0.45,-0.194,-0.336,-0.094
Naive,Seasonal Naive,0.425,0.335,0.52,-0.167,-0.288,-0.069
Naive,Naive,0.5,0.5,0.5,0.0,0.0,0.0
Naive,Drift,0.81,0.73,0.89,0.012,-0.012,0.035
Drift,Chronos-2,0.06,0.02,0.11,-0.831,-1.053,-0.644
Drift,TiRex,0.06,0.02,0.11,-0.688,-0.859,-0.531
Drift,TimesFM-2.5,0.08,0.03,0.14,-0.692,-0.883,-0.526
Drift,Toto-1.0,0.11,0.06,0.18,-0.646,-0.821,-0.487
Drift,Moirai-2.0,0.14,0.08,0.21,-0.624,-0.789,-0.47
Drift,Chronos-Bolt,0.1,0.05,0.17,-0.608,-0.77,-0.468
Drift,TabPFN-TS,0.13,0.06,0.2,-0.633,-0.819,-0.473
Drift,Sundial-Base,0.17,0.1,0.25,-0.57,-0.747,-0.411
Drift,Stat. Ensemble,0.11,0.05,0.18,-0.401,-0.539,-0.291
Drift,AutoARIMA,0.2,0.13,0.28,-0.331,-0.479,-0.21
Drift,AutoTheta,0.18,0.1,0.26,-0.327,-0.45,-0.233
Drift,AutoETS,0.32,0.23,0.41,-0.209,-0.347,-0.109
Drift,Seasonal Naive,0.3,0.21,0.4,-0.181,-0.312,-0.071
Drift,Naive,0.19,0.11,0.27,-0.013,-0.036,0.012
Drift,Drift,0.5,0.5,0.5,0.0,0.0,0.0