Beyond Static Leaderboards: Capability-Focused Evaluation with Structural Diversity for Time Series Foundation Models
Organizations: School of Software, BNRist, Tsinghua University · Timecho Ltd, Beijing, China · Harbin Institute of Technology
Abstract
Static public benchmarks for time series foundation models (TSFMs) typically have fixed and narrow test distributions. Their repeated reuse encourages benchmark-specific tuning, making reported performance reflect adaptation to the fixed test set rather than genuine forecasting generalization. In addition, a single aggregate score cannot fully characterize model capabilities across distinct temporal structures and input relationships. We propose CaFE (Capability-Focused Evaluation), a refreshable evaluation extension grounded in original benchmark data that enriches static benchmarks with structural diversity and enriches single-score black-box evaluation with multi-dimensional, capability-oriented assessment. CaFE first profiles the original benchmark and defines eight Structural Features (SFs) that characterize its temporal structure. For each SF, it resamples the original data according to its structural support, removes edge-of-distribution samples, and augments the retained samples by varying the SF's salience, producing samples with different structural profiles. After filtering out out-of-distribution samples while preserving diversity, CaFE yields a refreshed evaluation set. TSFMs are then evaluated on this set using both conventional forecast-error metrics and intervention-response metrics, giving each model a per-feature capability profile alongside endpoint accuracy. Experiments on GIFT-Eval and FEV-Mini20 show that CaFE yields stable evaluation results and reveals per-feature strengths and weaknesses that a single aggregate score hides. Moreover, on genuine data filtered by structural condition, models selected by CaFE outperform those chosen by the aggregate leaderboard. CaFE therefore makes model selection conditional on the structural response of interest.
Figures & tables
| Family | Original instances | Explicit structure | Paired change | Refresh |
|---|---|---|---|---|
| Retrospective suites | ||||
| TSFM suites | ||||
| Covariate-aware suites | ||||
| Observed-structure suites | ||||
| Live evaluation | ||||
| Synthetic mechanisms |
| Model | Probe MASE | Forecast-Change NRMSE |
|---|---|---|
| TimesFM 3.0 | 1.21 0.003 | 0.580 0.005 |
| TiREx-2 | 1.20 0.003 | 0.637 0.007 |
| Chronos-2 | 1.22 0.004 | 0.646 0.007 |
| Toto 2.0 | 1.24 0.004 | 0.671 0.004 |
| TimesFM 2.5 | 1.25 0.004 | 0.684 0.008 |
| Timer-3.5 | 1.28 0.005 | 0.788 0.009 |
Appendix figures & tables27 assets
Supplementary material from the paper’s appendix.
Appendix
| Structural feature | Controlled change | Control parameter | Applicability |
|---|---|---|---|
| SF1 Trend | Persistent directional continuation | Normalized trend magnitude | Uni./multi. |
| SF2 Multi-Seasonality | Concurrent stable periods | Number of active periods | Uni./multi. |
| SF3 Time-Varying Seasonality | Evolving amplitude or phase | Normalized evolution magnitude | Uni./multi. |
| SF4 Regime Switching | Bounded transition to a persistent state | Transition location | Uni./multi. |
| SF5 Intermittency | Sparse recurring events | Mean event gap | Uni./multi. |
| SF6 Common Factor | Shared trajectory across targets | Normalized shared-profile magnitude | Multi., targets |
| Suite | Horizon | Configurations | Models |
|---|---|---|---|
| GIFT-Eval Short | 30–60 | 55 | 11 |
| GIFT-Eval Medium | 480–600 | 21 | 10 |
| GIFT-Eval Long | 720–900 | 21 | 10 |
| fev-bench Mini-20 | 5–288 | 20 | 11 |
| Suite | Equal-weight diagnostic ranking |
|---|---|
| GIFT-Eval Short | 1. TimesFM 3.0 (0.925); 2. Toto 2.0 (0.625); 3. Chronos-2 (0.600); 4. TimesFM 2.5 (0.550); 5. Timer-3.5 (0.175); 6. Moirai 2 (0.125) |
| GIFT-Eval Medium | 1. TimesFM 3.0 (0.925); 2. Timer-3.5 (0.650); 3. Chronos-2 (0.600); 4. TimesFM 2.5 (0.375); 5. Toto 2.0 (0.300); 6. Moirai 2 (0.150) |
| GIFT-Eval Long | 1. TimesFM 3.0 (0.950); 2. Chronos-2 (0.600); 3. Timer-3.5 (0.600); 4. TimesFM 2.5 (0.400); 5. Toto 2.0 (0.375); 6. Moirai 2 (0.075) |
| fev-bench Mini-20 | 1. Chronos-2 (0.750); 2. TimesFM 3.0 (0.700); 3. TimesFM 2.5 (0.500); 4. Toto 2.0 (0.375); 5. Timer-3.5 (0.350); 6. Moirai 2 (0.325) |
| Suite | Configs | Models shown | Panel predictions |
|---|---|---|---|
| GIFT-Eval Short | 55 | 11 | 399,740 |
| GIFT-Eval Medium | 21 | 10 | 127,380 |
| GIFT-Eval Long | 21 | 10 | 121,810 |
| fev-bench Mini-20 | 20 | 11 | 121,902 |
| Suite | Lowest Probe MASE | Lowest Forecast-Change NRMSE |
|---|---|---|
| GIFT-Eval Short | TimesFM 3.0 (5/8); Toto 2.0 (2/8); Chronos-2 (1/8) | TimesFM 3.0 (4/8); Toto 2.0 (2/8); Linear Trend (1/8); TimesFM 2.5 (1/8) |
| GIFT-Eval Medium | TimesFM 3.0 (7/8); Chronos-2 (1/8) | TimesFM 3.0 (6/8); Chronos-2 (1/8); Linear Trend (1/8) |
| GIFT-Eval Long | TimesFM 3.0 (5/8); Timer-3.5 (2/8); Chronos-2 (1/8) | TimesFM 3.0 (6/8); Linear Trend (1/8); Timer-3.5 (1/8) |
| fev-bench Mini-20 | TimesFM 3.0 (7/8); TiREx-2 (1/8) | TimesFM 3.0 (3/8); Chronos-2 (1/8); Linear Trend (1/8); Naive (1/8); TimesFM 2.5 (1/8); Toto 2.0 (1/8) |
| Recommendation | Top-1 | Top-3 | Top-5 |
|---|---|---|---|
| Generic original MASE | 1/7 | 3/7 | 7/7 |
| Qualified original MASE | 1/7 | 4/7 | 7/7 |
| Capability-augmented MASE | 1/7 | 6/7 | 7/7 |
| Recommendation | Mean gain vs generic | Wins–ties–losses |
|---|---|---|
| Qualified original MASE | 11.02% | – |
| Capability-augmented MASE | 9.06% | 8–1–1 |
| Group or structural feature | Spearman |
|---|---|
| Multivariate | 1.00 |
| Univariate | 0.30 |
| Common factor | 1.00 |
| Cross-series dependence | 1.00 |
| Intermittency | 1.00 |
| Regime switching | 1.00 |
| Configuration–model | B | C |
|---|---|---|
| M4 Hourly–Transformer | 1.8348 | 9.3486 |
| M4 Hourly–DLinear | 3.0342 | 1.8950 |
| M4 Hourly–PatchTST | 1.4468 | 2.1678 |
| SZ Taxi–PatchTST | 0.6568 | 1.4263 |
| SZ Taxi–TSMixer | 0.9936 | 0.6860 |
| SF | Chronos-2 | Timer-3.5 | TimesFM 2.5 | TiREx-2 | Moirai 2 | Toto 2.0 | |
|---|---|---|---|---|---|---|---|
| SF1 | 18 | 2.132 / 0.082 | 1.966 / 0.243 | 1.898 / 0.216 | 1.843 / 0.256 | 2.152 / 0.215 | 1.876 / 0.243 |
| SF2 | 20 | 2.370 / 0.779 | 2.758 / 0.946 | 2.499 / 0.802 | 2.532 / 0.844 | 4.171 / 1.010 | 1.934 / 0.637 |
| SF3 | 19 | 1.526 / 0.529 | 1.738 / 0.674 | 1.462 / 0.679 | 1.484 / 0.580 | 1.853 / 0.740 | 1.572 / 0.571 |
| SF4 | 20 | 1.703 / 0.096 | 1.717 / 0.133 | 1.627 / 0.091 | 1.597 / 0.071 | 1.910 / 0.134 | 1.574 / 0.144 |
| SF5 | 20 | 2.929 / 0.905 | 2.872 / 0.914 | 2.833 / 0.837 | 2.745 / 0.972 | 4.211 / 0.965 | 2.699 / 0.955 |
| SF6 | 4 | 0.618 / 0.257 | 0.644 / 0.301 | 0.648 / 0.333 | 0.658 / 0.259 | 0.695 / 0.353 | 0.625 / 0.291 |
| Model | Official | SF1 | SF2 | SF3 | SF4 | SF5 | SF6 | SF7 | SF8 |
|---|---|---|---|---|---|---|---|---|---|
| Chronos-2 | 1.567 | 2.208/2.216 | 0.716/0.730 | 1.232/1.241 | 1.575/1.859 | 0.871/0.896 | 0.828/1.194 | 0.773/0.802 | 0.734/0.765 |
| TimesFM 2.5 | 1.601 | 2.140/2.220 | 0.713/0.722 | 1.244/1.246 | 1.911/2.318 | 0.969/1.052 | 0.828/1.232 | 0.782/0.813 | 0.745/0.782 |
| TimesFM 3.0 | 1.464 | 2.003/2.050 | 0.667/0.686 | 1.166/1.165 | 1.628/1.916 | 0.885/0.923 | 0.807/1.188 | 0.748/0.772 | 0.697/0.732 |
| TiREx-2 | 1.610 | 2.239/2.216 | 0.706/0.732 | 1.241/1.246 | 1.722/1.914 | 0.876/0.921 | 0.838/1.233 | 0.788/0.817 | 0.751/0.801 |
| Moirai 2 | 1.701 | 2.258/2.260 | 0.766/0.797 | 1.353/1.372 | 1.688/1.998 | 0.904/1.030 | 0.922/1.327 | 0.824/0.863 | 0.809/0.877 |
| Model | Official | SF1 | SF2 | SF3 | SF4 | SF5 | SF6 | SF7 | SF8 |
|---|---|---|---|---|---|---|---|---|---|
| Timer-3.5 | 1.757 | 2.534/2.644 | 0.711/0.741 | 1.185/1.182 | 1.644/1.931 | 0.865/0.899 | 0.855/1.260 | 0.797/0.828 | 0.723/0.772 |
| Toto 2.0 | 1.452 | 1.971/2.065 | 0.673/0.700 | 1.186/1.177 | 1.580/1.848 | 0.934/0.963 | 0.837/1.220 | 0.771/0.793 | 0.690/0.726 |
| Naive | 2.579 | 3.531/4.370 | 1.543/1.891 | 2.041/2.015 | 2.210/2.595 | 1.064/1.237 | 1.215/1.779 | 1.171/1.239 | 1.678/2.001 |
| Seasonal Naive | 2.193 | 2.945/3.920 | 1.276/1.549 | 1.722/1.728 | 1.953/2.313 | 1.045/1.254 | 1.143/1.659 | 1.086/1.137 | 1.250/1.335 |
| Drift | 2.565 | 3.431/3.431 | 1.542/1.897 | 2.060/2.036 | 2.631/3.269 | 1.100/1.283 | 1.248/1.821 | 1.191/1.258 | 1.686/2.012 |
| Linear Trend | 4.806 | 8.074/8.074 | 2.211/2.449 | 2.566/2.585 | 5.219/7.105 | 1.599/1.867 | 2.155/3.016 | 1.905/2.028 | 1.841/2.168 |
| Model | SF1 | SF2 | SF3 | SF4 | SF5 | SF6 | SF7 | SF8 |
|---|---|---|---|---|---|---|---|---|
| Chronos-2 | 1.371 | 0.437 | 0.655 | 0.401 | 0.991 | 0.392 | 0.427 | 0.420 |
| TimesFM 2.5 | 1.506 | 0.472 | 0.677 | 0.396 | 0.901 | 0.419 | 0.537 | 0.475 |
| TimesFM 3.0 | 1.179 | 0.340 | 0.624 | 0.387 | 0.928 | 0.392 | 0.403 | 0.389 |
| TiREx-2 | 1.119 | 0.534 | 0.650 | 0.403 | 0.941 | 0.418 | 0.497 | 0.504 |
| Moirai 2 | 2.109 | 0.609 | 0.642 | 0.419 | 1.024 | 0.449 | 0.609 | 0.617 |
| Model | SF1 | SF2 | SF3 | SF4 | SF5 | SF6 | SF7 | SF8 |
|---|---|---|---|---|---|---|---|---|
| Timer-3.5 | 2.229 | 0.498 | 0.678 | 0.423 | 0.965 | 0.442 | 0.545 | 0.454 |
| Toto 2.0 | 1.611 | 0.479 | 0.624 | 0.397 | 0.951 | 0.422 | 0.433 | 0.386 |
| Naive | 1.000 | 1.156 | 0.750 | 0.560 | 1.091 | 0.554 | 0.650 | 0.789 |
| Seasonal Naive | 2.213 | 1.020 | 0.747 | 0.532 | 1.068 | 0.563 | 0.628 | 0.760 |
| Drift | 1.175 | 0.753 | 0.578 | 1.112 | 0.560 | 0.657 | 0.794 | |
| Linear Trend | 1.079 | 1.002 | 0.711 | 1.174 | 0.920 | 1.354 | 0.880 |
| Model | SF | Tasks | 95% interval | |
|---|---|---|---|---|
| Chronos-2 | SF6 | 13 | -0.020 | [-0.113, 0.052] |
| Chronos-2 | SF7 | 12 | 0.000 | [-0.119, 0.113] |
| Chronos-2 | SF8 | 8 | 0.006 | [0.000, 0.013] |
| TimesFM 3.0 | SF6 | 13 | 0.157 | [0.064, 0.259] |
| TimesFM 3.0 | SF7 | 11 | 0.051 | [-0.020, 0.160] |
| TimesFM 3.0 | SF8 | 7 | 0.003 | [-0.000, 0.009] |
| SF | Chronos-2 | Timer-3.5 | TimesFM 2.5 | TiREx-2 | Moirai 2 | Toto 2.0 | |
|---|---|---|---|---|---|---|---|
| SF1 | 9 | 2.982 / 0.051 | 2.808 / 0.264 | 2.880 / 0.259 | – | 3.469 / 0.293 | 12.785 / 0.590 |
| SF2 | 11 | 5.309 / 1.102 | 5.533 / 1.206 | 4.016 / 0.961 | – | 10.671 / 1.729 | 10.488 / 1.131 |
| SF3 | 10 | 7.051 / 0.787 | 7.292 / 1.130 | 3.507 / 0.980 | – | 10.616 / 1.565 | 9.955 / 1.296 |
| SF4 | 11 | 2.378 / 0.053 | 2.581 / 0.191 | 2.453 / 0.131 | – | 4.026 / 0.276 | 7.597 / 0.176 |
| SF5 | 11 | 2.851 / 1.402 | 3.039 / 1.738 | 2.936 / 1.322 | – | 3.592 / 1.115 | 6.459 / 1.556 |
| SF6 | 4 | 0.919 / 0.257 | 0.952 / 0.474 | 0.966 / 0.524 | – | 1.324 / 0.571 | 1.163 / 0.377 |
| SF | Chronos-2 | Timer-3.5 | TimesFM 2.5 | TiREx-2 | Moirai 2 | Toto 2.0 | |
|---|---|---|---|---|---|---|---|
| SF1 | 10 | 3.597 / 0.062 | 3.549 / 0.191 | 3.682 / 0.124 | – | 4.609 / 0.213 | 16.115 / 0.257 |
| SF2 | 11 | 6.252 / 0.914 | 6.780 / 1.168 | 4.890 / 0.966 | – | 9.542 / 1.638 | 21.869 / 0.998 |
| SF3 | 10 | 4.860 / 0.859 | 8.021 / 1.223 | 5.632 / 0.961 | – | 9.717 / 1.190 | 23.432 / 1.119 |
| SF4 | 11 | 2.934 / 0.064 | 3.100 / 0.175 | 3.253 / 0.106 | – | 4.442 / 0.326 | 16.994 / 0.265 |
| SF5 | 11 | 3.131 / 1.051 | 3.087 / 1.118 | 3.185 / 1.069 | – | 4.636 / 1.683 | 16.407 / 1.184 |
| SF6 | 4 | 1.039 / 0.385 | 1.144 / 0.739 | 1.113 / 0.772 | – | 1.749 / 1.084 | 1.324 / 0.663 |
| SF | Chronos-2 | Timer-3.5 | TimesFM 2.5 | TiREx-2 | Moirai 2 | Toto 2.0 | |
|---|---|---|---|---|---|---|---|
| SF1 | 18 | 1.938 / 0.176 | 1.807 / 0.181 | 1.469 / 0.111 | 1.736 / 0.130 | 1.625 / 0.087 | 1.591 / 0.124 |
| SF2 | 20 | 2.656 / 1.202 | 3.003 / 1.143 | 2.582 / 0.954 | 2.703 / 1.042 | 3.144 / 1.213 | 1.839 / 0.809 |
| SF3 | 20 | 2.190 / 0.812 | 2.140 / 0.756 | 1.744 / 0.734 | 2.040 / 0.794 | 2.045 / 0.797 | 1.659 / 0.663 |
| SF4 | 20 | 1.913 / 0.213 | 1.917 / 0.163 | 1.562 / 0.120 | 1.853 / 0.136 | 1.647 / 0.103 | 1.603 / 0.110 |
| SF5 | 18 | 2.188 / 0.934 | 1.987 / 0.963 | 1.712 / 0.864 | 2.154 / 0.894 | 2.055 / 1.062 | 1.731 / 0.852 |
| SF6 | 9 | 1.766 / 0.286 | 2.044 / 0.359 | 1.630 / 0.301 | 1.819 / 0.291 | 1.791 / 0.380 | 1.663 / 0.295 |
| Suite | Models | |||
|---|---|---|---|---|
| GIFT-Eval Short | 6 | 0.943 | -0.086 | 0.029 |
| GIFT-Eval Medium | 5 | 0.700 | 0.800 | 0.800 |
| GIFT-Eval Long | 5 | 0.900 | 0.800 | 0.900 |
| fev-bench Mini-20 | 6 | 0.657 | 0.543 | 0.771 |
| SF | Unanimous / 5 | Mean modal | Min modal | Setting-modal models |
|---|---|---|---|---|
| SF1 | 5 | 1.00 | 1.00 | Chronos-2 (5) |
| SF2 | 0 | 0.82 | 0.70 | TimesFM 2.5 (1), Toto 2.0 (4) |
| SF3 | 5 | 1.00 | 1.00 | Chronos-2 (5) |
| SF4 | 0 | 0.68 | 0.50 | TiREx-2 (3), TimesFM 2.5 (1), Chronos-2 (1) |
| SF5 | 0 | 0.74 | 0.50 | TimesFM 2.5 (4), Chronos-2 (1) |
| SF6 | 0 | 0.64 | 0.50 | Chronos-2 (5) |
| Suite | SF | Model | Tasks | MASE [95% interval] | Task median | Positive tasks |
|---|---|---|---|---|---|---|
| GIFT-Eval Short | SF6 | Chronos-2 | 4 | 0.038 [0.009, 0.068] | 0.042 | 3/4 |
| GIFT-Eval Short | SF6 | TiREx-2 | 4 | -0.004 [-0.006, -0.001] | -0.005 | 1/4 |
| GIFT-Eval Short | SF6 | Toto 2.0 | 4 | 0.005 [-0.012, 0.030] | -0.004 | 2/4 |
| GIFT-Eval Short | SF7 | Chronos-2 | 8 | 0.012 [-0.001, 0.030] | 0.002 | 6/8 |
| GIFT-Eval Short | SF7 | TiREx-2 | 8 | 0.003 [-0.002, 0.008] | 0.001 | 5/8 |
| GIFT-Eval Short | SF7 | Toto 2.0 | 8 | 0.031 [-0.002, 0.077] | -0.001 | 4/8 |
| Step | Official MASE | Official FC-NRMSE | FC-NRMSE-objective MASE | FC-NRMSE-objective |
|---|---|---|---|---|
| 0 | 0.725 | 0.641 | 0.725 | 0.641 |
| 1k | 0.681 | 0.593 | 0.778 | 0.533 |
| 2k | 0.665 | 0.556 | 0.804 | 0.488 |
| 3k | 0.655 | 0.582 | 0.816 | 0.473 |
| 4k | 0.645 | 0.587 | 0.815 | 0.483 |
| 5k | 0.641 | 0.606 | 0.814 | 0.477 |
| Panel | Evaluation setting | Main support | Provenance |
|---|---|---|---|
| GIFT-Eval Short latest | Frozen latest Short panel | 55 configurations; 3 unordered variants; 11 models | Analysis record |
| GIFT-Eval Medium latest | Frozen latest Medium panel | 21 configurations; 10 models | Analysis record |
| GIFT-Eval Long latest | Frozen latest Long panel | 21 configurations; 10 models | Analysis record |
| fev-bench Mini-20 latest | Frozen latest Mini-20 panel | 20 configurations; 11 models | Analysis record |
| Input removal | Matched full-input and target-only views | Same treatment contracts; assessed target history and future fixed | Separate block |
| Stability (latest) | Five augmentation seeds on Short | 55 configurations; 7 models | Analysis record |
| Claim family | Evaluation evidence | Result presentation |
|---|---|---|
| SF1–SF8 interventions | Structural constructions and their ordered control settings | Feature-level response profiles and heatmaps |
| Generated-sample accuracy and response | Four evaluation panels with suite-specific support | MASE and Forecast-Change NRMSE tables |
| Structural-response profiles | Feature-local comparisons on the eligible model support | Main and supplementary heatmaps |
| Refresh stability | Five-seed and earlier fixed-panel comparisons | Stability summary and figure |
| Auxiliary-input utility | Matched full-input and target-only comparisons | Auxiliary-Input Gap table and figure |
| Training-objective trade-off | Two objectives trained on the same sample set | Fine-tuning curves and objective comparison |
| Suite | Configs | Candidates/References | Generated samples | Models | Predictions | Failures | Horizon |
|---|---|---|---|---|---|---|---|
| GIFT-Eval Short | 55 | 15,745 | 17,773 | 11 | 399,740 | 0 | 30–60 |
| GIFT-Eval Medium | 21 | 4,259 | 6,875 | 10 | 127,380 | 0 | 480–600 |
| GIFT-Eval Long | 21 | 4,179 | 6,552 | 10 | 121,810 | 0 | 720–900 |
| fev-bench Mini-20 | 20 | 2,809 | 5,609 | 11 | 121,902 | 0 | 5–288 |
| Level | Declared environment | Purpose |
|---|---|---|
| Summary consistency | Linux or macOS; CPU; less than 1 GB memory and disk | Checks row counts, dimensions, and numerical agreement for representative tables and figures |
| Table and figure reconstruction | Linux or macOS; Python 3.11 or later; 4 CPU cores, 8 GB RAM, and 5 GB free disk recommended | Recomputes the four analysis blocks reported in the paper from compact numerical summaries |
| End-to-end evaluation | Linux x86-64; Python 3.12; CUDA 12.8-compatible NVIDIA driver; 32 GB VRAM per worker; 16 CPU cores and 64 GB RAM recommended | Defines the environment for reconstructing treatments, evaluating the models, and recomputing the reported analyses |
Forecasting Benchmarks
Forecasting Benchmarks are datasets and evaluation protocols for comparing predictions of future time-series values, events, and outcomes.
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