Time series forecasting on GIFT-Eval (test)
0.675MASEFedTRL
Evaluation results
| Method | Links | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| FedTRLType=Zero-Shot Models (FL), Zero-shot=true2026.04 | 0.675 | — | — | — | — | — | — | — | — | 0.46 | 8.676 | — | — | — | — | — | — | — | — | — | — | — | |
| TimesFMType=Zero-Shot Models, Zero-shot=true2026.04 | 0.68 | — | — | — | — | — | — | — | — | 0.465 | 8.237 | — | — | — | — | — | — | — | — | — | — | — | |
| TabPFNType=Zero-Shot Models, Zero-shot=true2026.04 | 0.748 | — | — | — | — | — | — | — | — | 0.48 | 8.268 | — | — | — | — | — | — | — | — | — | — | — | |
| PTST.Type=Supervised Task-Specific Models, Zero-shot=true2026.04 | 0.762 | — | — | — | — | — | — | — | — | 0.496 | 10.052 | — | — | — | — | — | — | — | — | — | — | — | |
| FFTSType=Zero-Shot Models (FL), Zero-shot=true2026.04 | 0.766 | — | — | — | — | — | — | — | — | 0.521 | 9.787 | — | — | — | — | — | — | — | — | — | — | — | |
| ChronosType=Zero-Shot Models, Zero-shot=true2026.04 | 0.786 | — | — | — | — | — | — | — | — | 0.551 | 14.309 | — | — | — | — | — | — | — | — | — | — | — | |
| iTrans.Type=Supervised Task-Specific Models, Zero-shot=true2026.04 | 0.802 | — | — | — | — | — | — | — | — | 0.524 | 11.32 | — | — | — | — | — | — | — | — | — | — | — | |
| MoiraiType=Zero-Shot Models, Zero-shot=true2026.04 | 0.809 | — | — | — | — | — | — | — | — | 0.515 | 10.175 | — | — | — | — | — | — | — | — | — | — | — | |
| N-BEATSType=Supervised Task-Specific Models, Zero-shot=true2026.04 | 0.842 | — | — | — | — | — | — | — | — | 0.689 | 21.381 | — | — | — | — | — | — | — | — | — | — | — | |
| FedAvgType=Zero-Shot Models (FL), Zero-shot=true2026.04 | 0.872 | — | — | — | — | — | — | — | — | 0.7 | 18.231 | — | — | — | — | — | — | — | — | — | — | — | |
| Auto ARIMAType=Statistical Methods, Zero-shot=true2026.04 | 0.964 | — | — | — | — | — | — | — | — | 0.77 | 21.515 | — | — | — | — | — | — | — | — | — | — | — | |
| Auto ThetaType=Statistical Methods, Zero-shot=true2026.04 | 0.978 | — | — | — | — | — | — | — | — | 1.051 | 24.031 | — | — | — | — | — | — | — | — | — | — | — | |
| TiDEType=Supervised Task-Specific Models, Zero-shot=true2026.04 | 0.98 | — | — | — | — | — | — | — | — | 0.652 | 18.557 | — | — | — | — | — | — | — | — | — | — | — | |
| Seasonal NaiveType=Statistical Methods, Zero-shot=true2026.04 | 1 | — | — | — | — | — | — | — | — | 1 | 26.175 | — | — | — | — | — | — | — | — | — | — | — | |
| DeepARType=Supervised Task-Specific Models, Zero-shot=true2026.04 | 1.206 | — | — | — | — | — | — | — | — | 0.721 | 18.938 | — | — | — | — | — | — | — | — | — | — | — | |
| NaiveType=Statistical Methods, Zero-shot=true2026.04 | 1.26 | — | — | — | — | — | — | — | — | 1.383 | 28.072 | — | — | — | — | — | — | — | — | — | — | — | |
| Chronos-2Horizon (h)=642026.05 | 5.709 | — | — | — | — | — | — | — | — | 102.4 | — | 255,127 | 132 | 156.2 | 0.46 | 0.376 | 2.48 | 44.1 | 888,025 | 69 | 25.5 | — | |
| Chronos-BoltHorizon (h)=642026.05 | 6.068 | — | — | — | — | — | — | — | — | 101.9 | — | 251,450 | 131.7 | 156.8 | 0.504 | 0.416 | 1.55 | 45.2 | 587,680 | 67.2 | 22.7 | — | |
| Chronos-T5Horizon (h)=642026.05 | 6.291 | — | — | — | — | — | — | — | — | 115.2 | — | 292,023 | 147.4 | 173.7 | 0.484 | 0.393 | 5.84 | 46.2 | 1.98 | 65 | 19.1 | — | |
| NanoTS (Full Finetune)Initialization=Language-pretrained (Qwen3-0.6B), Training Regime=Full Finetune, Horizon (h)=64, Training step=1282026.05 | 6.424 | — | — | — | — | — | — | — | — | 119 | — | 271,341 | 143.7 | 168.2 | 0.586 | 0.495 | 2.85 | 48.3 | 696,208 | 54 | 2.6 | — | |
| NanoTS (IO Only)Initialization=Language-pretrained (Qwen3-0.6B), Training Regime=IO Only, Horizon (h)=64, Training step=1282026.05 | 6.502 | — | — | — | — | — | — | — | — | 141.5 | — | 319,226 | 147.9 | 174.9 | 0.557 | 0.462 | 2.68 | 50.3 | 1.32 | 61.2 | 1.5 | — | |
| NanoTS (LoRA Attn)Initialization=Language-pretrained (Qwen3-0.6B), Training Regime=LoRA Attn, Horizon (h)=64, Training step=1282026.05 | 6.602 | — | — | — | — | — | — | — | — | 137.2 | — | 259,652 | 140.8 | 164 | 0.581 | 0.487 | 5.39 | 50.5 | 2.27 | 55.5 | 2.9 | — | |
| ARIMAHorizon (h)=642026.05 | 6.609 | — | — | — | — | — | — | — | — | 116.6 | — | 345,041 | 145.4 | 171.8 | 0.534 | 0.446 | 5.8 | 47.8 | 2.27 | 60.8 | 10.5 | — | |
| NanoTS (LoRA Attn+IO)Initialization=Language-pretrained (Qwen3-0.6B), Training Regime=LoRA Attn+IO, Horizon (h)=64, Training step=1282026.05 | 6.628 | — | — | — | — | — | — | — | — | 138.8 | — | 265,546 | 144 | 169 | 0.566 | 0.473 | 2.82 | 48.5 | 1.36 | 57.1 | 5.2 | — | |
| NanoTS (IO Only)Initialization=Random, Training Regime=IO Only, Horizon (h)=64, Training step=1282026.05 | 7.341 | — | — | — | — | — | — | — | — | 141.3 | — | 445,540 | 183.5 | 205 | 0.563 | 0.478 | 1.17 | 51.7 | 394,850 | 65.3 | 3.6 | — | |
| NanoTS (Full Finetune)Initialization=Random, Training Regime=Full Finetune, Horizon (h)=64, Training step=1282026.05 | 7.7 | — | — | — | — | — | — | — | — | 168.9 | — | 583,696 | 210.5 | 232.7 | 0.575 | 0.494 | 693,452 | 53.4 | 377,358 | 64.2 | 0.9 | — | |
| NanoTS (LoRA Attn)Initialization=Random, Training Regime=LoRA Attn, Horizon (h)=64, Training step=1282026.05 | 7.77 | — | — | — | — | — | — | — | — | 171.4 | — | 592,435 | 212.3 | 234.7 | 0.579 | 0.499 | 583,786 | 53.6 | 339,884 | 63.9 | 0.1 | — | |
| NanoTS (LoRA Attn+IO)Initialization=Random, Training Regime=LoRA Attn+IO, Horizon (h)=64, Training step=1282026.05 | 7.812 | — | — | — | — | — | — | — | — | 137.9 | — | 346,961 | 166.8 | 190.5 | 0.719 | 0.628 | 55,012 | 56.9 | 104,026 | 50.2 | 3 | — | |
| Chronos2(Data leakage)Params=120M, Status=Data leakage2026.02 | 69.8 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| TimesFM-2.5Params=200M, Zero-shot=true2026.02 | 70.5 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| PatchTST-FMParams=260M, Zero-shot=true2026.02 | 70.7 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Xihe-MaxParams=1.5B, Zero-shot=true2026.02 | 71.1 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| ReversoParams=2.6M, Zero-shot=true2026.02 | 71.1 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| TiRexParams=30M, Zero-shot=true2026.02 | 71.6 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Xihe-BaseParams=700M, Zero-shot=true2026.02 | 71.8 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Chronos2Params=120M, Zero-shot=true2026.02 | 72 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Xihe-FlashParams=300M, Zero-shot=true2026.02 | 72.6 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Reverso-SmallParams=0.6M, Zero-shot=true2026.02 | 72.6 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| FlowState-9.1MParams=9.1M, Zero-shot=true2026.02 | 72.6 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Moirai2Params=11M, Zero-shot=true2026.02 | 72.8 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Xihe-LiteParams=94M, Zero-shot=true2026.02 | 72.9 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| FlowState-2.6MParams=2.6M, Zero-shot=true2026.02 | 73.5 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Kairos-50MParams=50M, Zero-shot=true2026.02 | 74.2 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Kairos-23MParams=23M, Zero-shot=true2026.02 | 74.8 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Toto-BaseParams=150M, Zero-shot=true2026.02 | 75 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Sundial-BParams=128M, Zero-shot=true2026.02 | 75 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Kairos-10MParams=10M, Zero-shot=true2026.02 | 75.3 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| TTM-FinetunedParams=1.0M, Training Mode=Finetuned2026.02 | 75.6 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| TimesFM-2.0Params=500M, Zero-shot=true2026.02 | 75.8 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Reverso-NanoParams=0.2M, Zero-shot=true2026.02 | 76 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Xihe-TinyParams=9.5M, Zero-shot=true2026.02 | 76.6 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| TabPFN-TSParams=11M, Zero-shot=true2026.02 | 77.1 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| YingLong-300MParams=300M, Zero-shot=true2026.02 | 79.8 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| YingLong-110MParams=100M, Zero-shot=true2026.02 | 80.9 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Chronos-Bolt-SParams=48M, Zero-shot=true2026.02 | 82.2 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| YingLong-50MParams=50M, Zero-shot=true2026.02 | 82.2 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| SuperLinearParams=2.5M, Zero-shot=true2026.02 | 85.7 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Moirai-LParams=311M, Zero-shot=true2026.02 | 87.5 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Chronos-BParams=200M, Zero-shot=true2026.02 | 87.6 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| YingLong-6MParams=6.0M, Zero-shot=true2026.02 | 88 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Moirai-BParams=91M, Zero-shot=true2026.02 | 90.1 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Moirai-SParams=14M, Zero-shot=true2026.02 | 94.6 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Qwen3 TextHorizon (h)=642026.05 | 9,911 | — | — | — | — | — | — | — | — | 489.1 | — | 213.1 | 489.1 | 720.8 | 5,672 | 824.6 | 3.23 | 56.8 | 1.62 | 58.9 | 4.8 | — | |
| Auto ArimaModel Category=Statistical Models2026.02 | — | 3.5 | 7.53 | 4.6 | 9.67 | 8.25 | 10.93 | 10.45 | 8.62 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Auto ETSModel Category=Statistical Models2026.02 | — | 5.67 | 10.59 | 4.8 | 11.93 | 12.5 | 13.07 | 11.75 | 10.9 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Auto ThetaModel Category=Statistical Models2026.02 | — | 4.5 | 11.75 | 8 | 11.73 | 9 | 13.47 | 8.15 | 10.52 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| CrossformerModel Category=Deep Learning2026.02 | — | 16 | 9.62 | 11.6 | 7.6 | 15.75 | 8 | 7.75 | 9.42 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| DeepARModel Category=Deep Learning2026.02 | — | 9.83 | 9.56 | 6.8 | 6.93 | 3 | 4.4 | 8.1 | 7.66 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| DLinearModel Category=Deep Learning2026.02 | — | 11.67 | 9.03 | 10 | 8.8 | 8.75 | 9.53 | 8.8 | 9.23 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Empirical GPModel Category=Statistical Models2026.02 | — | 8.67 | 7.72 | 5.2 | 7.73 | 8.5 | 5.87 | 8.5 | 7.56 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Gaussian RBF GPModel Category=Statistical Models2026.02 | — | 14.83 | 11.97 | 13.8 | 10.73 | 10.75 | 12.2 | 13.55 | 12.36 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| iTransformerModel Category=Deep Learning2026.02 | — | 4.17 | 4.34 | 6.2 | 2.93 | 2.25 | 3.4 | 3.35 | 3.77 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| MoiraiAgentAdditional learning cost=fine-tune 3B LLM, Router size=3B LLM, Inference latency=472.6 ms2026.06 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | 68.87 | |
| N-BEATSModel Category=Deep Learning2026.02 | — | 7.83 | 9.19 | 9.2 | 8.73 | 6.5 | 7.67 | 6.9 | 8.22 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| NaiveModel Category=Statistical Models2026.02 | — | 10.17 | 12.75 | 12.4 | 14.53 | 14.75 | 15.27 | 11.65 | 13.09 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| PatchTSTModel Category=Deep Learning2026.02 | — | 3.33 | 3.16 | 4.8 | 2.73 | 1.75 | 3.4 | 3 | 3.13 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Seasonal NaiveModel Category=Statistical Models2026.02 | — | 7.5 | 7.88 | 9.4 | 11.93 | 13.25 | 11.27 | 9.7 | 9.68 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| Spectral Mixture GPModel Category=Statistical Models2026.02 | — | 13.17 | 10.53 | 14 | 9.2 | 9.5 | 9.2 | 12.7 | 10.87 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| SynapseAdditional learning cost=training-free adaptive ensemble2026.06 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | 69.86 | |
| TFTModel Category=Deep Learning2026.02 | — | 3.83 | 4.22 | 5.6 | 3 | 3.25 | 2.53 | 4.65 | 3.87 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| TiDEModel Category=Deep Learning2026.02 | — | 11.33 | 6.16 | 9.6 | 7.8 | 8.25 | 5.8 | 7 | 7.11 | — | — | — | — | — | — | — | — | — | — | — | — | — | |
| TimeCopilotAdditional learning cost=no training; LLM agent, Router size=LLM-scale, Inference latency=≥ 450 ms2026.06 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | 70.51 | |
| TimeRouterAdditional learning cost=∼ 110 s CPU, Router size=1.72 MB, Inference latency=9.9 ms2026.06 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | 67.65 | |
| TSOrchestraAdditional learning cost=fine-tune reasoning LLM (R1-style), Router size=3B LLM, Inference latency=≥ 472.6 ms2026.06 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | 67.68 | |
| ZooCastAdditional learning cost=train co-embedding selector2026.06 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | 69.2 |