LiveHouse-TS: An Open-world Living Benchmark for Time Series Foundation Models
Organizations: Shanghai Innovation Institute · The Hong Kong University of Science and Technology (Guangzhou)
Abstract
Time Series Foundation Models (TSFMs) have recently emerged as a highly promising paradigm for cross-domain zero-shot forecasting. However, existing evaluation protocols predominantly rely on static benchmarks with fixed historical test windows. While these benchmarks provide a valuable baseline snapshot, they evaluate an average performance on a fixed history, failing to capture how models behave in continuously evolving real-world environments characterized by seasonal variations, distribution shifts, and unexpected events. To bridge this gap, we introduce LiveHouse-TS, the first open-world living benchmark infrastructure for TSFMs. By evaluating models prequentially on real future data in open-world environments, LiveHouse-TS shifts time series benchmarking from snapshot accuracy to continuous temporal validity. Rather than acting as a one-off leaderboard, our infrastructure serves as a continuous time series infrastructure designed to explore vital, long-term scientific questions: Can model rankings be maintained over the long term? Which models remain genuinely robust under distribution shifts? Extensive streaming evaluations across 11 domains with 17 datasets demonstrate that static rankings undergo a dramatic reshuffling under a live protocol.
Figures & tables
| Benchmark | Year | Dataset | Evaluation | Leaderboard | |||||||
| Live/Static | #Domain | #Data | LR | Test zero-shot? | FT | Multivariate | RTL | OND | Metrics | ||
| Monash ( Godahewa et al., 2021 ) | 2021 | Static | 7 | 20 | ✘ | ✘ | Point | ✘ | ✘ | ✘ | MASE, sMAPE, msMAPE, MAE, RMSE |
| BasicTS ( Shao et al., 2023 ) | 2023 | Static | 5 | 20 | ✘ | ✘ | point | ✔ | ✘ | ✘ | MAE, RMSE, MAPE, WAPE |
| TFB ( Qiu et al., 2024 ) | 2024 | Static | 10 | 41 | ✘ | ✘ | Point | ✔ | ✘ | ✔ | MAE, MSE, MASE, MSMAPE |
| ProbTS ( Zhang et al., 2024 ) | 2024 | Static | 6 | 12 | ✘ | ✔ | Point/Prob. | ✔ | ✘ | ✘ | NMAE, CRPS |
| CiK ( Williams et al., 2025 ) | 2025 | Static | 7 | 9 | ✘ | ✔ | Prob. | ✘ | ✘ | ✘ | CRPS |
| Group | # | Domains | Native freq. | Eval freq. | Sources | Targets |
|---|---|---|---|---|---|---|
| Environment | 5 | weather, air quality, weather-energy | 1h (4), 1d | 1h (4), 1d | Open-Meteo, NASA POWER, NWS, NOAA NCEI | temperature, PM 2.5 |
| Water | 3 | hydrology, ocean | 6min, 10min, 15min | 1h | USGS Water, NOAA CO-OPS, NOAA NDBC | discharge, water level, wave height |
| Mobility | 1 | traffic | 15min | 15min | GBFS Citi Bike | available bikes |
| Finance | 4 | finance | 1s, 1h (2), 1mo | 1s, 1h (2), 1mo | Binance, CoinGecko | close, market price |
| Society/economy | 2 | web attention, macro-economy | 1d, 1y | 1d, 1y | Wikimedia, World Bank | pageviews, GDP |
| Events | 2 | news events, disaster events | 15min, 1h | 1d | GDELT, USGS Earthquake | event volume, count |
| Measure | Metric | Foundation models | Classical baselines | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Moi2 | TFM | Chr2 | TiRex | TabPFN | Sundial | ChrB | Toto1 | ARIMA | MovAvg | ETS | SNaive | ||
| Average Rank ( ) | RMSE | 4.70 | 3.30 | 3.80 | 4.00 | 5.80 | 6.40 | 7.10 | 10.70 | 7.45 | 7.75 | 8.00 | 9.00 |
| MAPE | 3.70 | 3.85 | 4.90 | 4.30 | 5.10 | 6.45 | 6.15 | 5.05 | 8.70 | 9.65 | 9.80 | 10.35 | |
| CRPS | 2.30 | 9.20 | 7.25 | 7.05 | 4.70 | 3.15 | 3.90 | 2.95 | 8.70 | 9.35 | 9.45 | 10.00 | |
| Win Rate ( ) | RMSE | 0.66 | 0.79 | 0.75 | 0.73 | 0.56 | 0.51 | 0.45 | 0.12 | 0.41 | 0.39 | 0.36 | 0.27 |
| MAPE | 0.76 | 0.74 | 0.65 | 0.70 | 0.63 | 0.51 | 0.53 | 0.63 | 0.30 | 0.21 | 0.20 | 0.15 | |
Appendix figures & tables19 assets
Supplementary material from the paper’s appendix.
Appendix
| Dataset | Domain | Entity & region | Primary target | Public endpoint | Background notes |
|---|---|---|---|---|---|
| Open-Meteo Shanghai weather | weather | Shanghai grid (31.23 ∘ N, 121.47 ∘ E) | 2 m temperature | https://api.open-meteo.com/v1/forecast | Smooth diurnal weather; humidity, wind, precipitation covariates |
| Open-Meteo Shanghai air quality | air quality | Shanghai grid | PM 2.5 | https://air-quality-api.open-meteo.com/v1/air-quality | Pollutant spikes; PM 10 , NO 2 , CO covariates |
| NASA POWER Shanghai meteorology | weather-energy | Shanghai point | Air temperature (T2M) | https://power.larc.nasa.gov/api/temporal/hourly/point | Energy-oriented meteorology; evaluated daily despite hourly native series |
| USGS Potomac discharge | hydrology | USGS site 01646500, Potomac River | River discharge | https://waterservices.usgs.gov/nwis/iv/ | High-frequency hydrology; gauge height covariate |
| NOAA CO-OPS San Francisco water level | ocean | Tide station 9414290, San Francisco | Water level | https://api.tidesandcurrents.noaa.gov/api/prod/datagetter | Six-minute coastal measurements with tide-like oscillation |
| NOAA NDBC buoy 46013 | ocean | NDBC buoy 46013 | Significant wave height | https://www.ndbc.noaa.gov/data/realtime2/46013.txt | Marine buoy observations; wind, pressure, temperature covariates |
| Dataset | Domain | Data freq. | Eval freq. | Target | Hist. | Hor. | Type | Mean | Std | Range | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Open-Meteo weather | weather | 1h | 1h | temperature_2m | 336 | 24 | direct | 32 | 26.97 | 2.746 | 24.0–33.7 |
| Open-Meteo air quality | air_quality | 1h | 1h | pm2_5 | 336 | 24 | direct | 32 | 50.68 | 22.38 | 27.1–99.4 |
| NASA POWER meteorology | weather_energy | 1h | 1d | T2M | 336 | 24 | direct | 112 | 23.62 | 3.679 | 17.4–30.9 |
| USGS Potomac water | hydrology | 15min | 1h | usgs_00060 | 96 | 24 | direct | 275 | 9,824 | 652.9 | 8,770–11,100 |
| NOAA CO-OPS water level | ocean | 6min | 1h | water_level | 240 | 60 | direct | 240 | 1.012 | 0.558 | 0.042–1.84 |
| NOAA NDBC buoy | ocean | 10min | 1h | wave_height | 144 | 72 | direct | 76 | 2.034 | 0.187 | 1.8–2.4 |
| Domain group | Observed pattern in verification samples |
|---|---|
| Weather & air quality | Diurnal structure (Open-Meteo, NWS) and pollutant spikes (PM 2.5 ) |
| Weather-energy | Smooth exogenous meteorology suitable as covariate-rich context |
| Hydrology & ocean | Slower physical dynamics; sub-hourly coastal tides and buoy waves |
| Urban mobility | System-level bike availability rises/falls with commuting demand |
| Finance | Heavy-tailed movement from 1 s to monthly BTC series; CoinGecko adds market-level context |
| Web & macro | Sparse daily pageviews and slow annual GDP growth with long history |
| Dataset | Domain | CV | Observed dynamic pattern | |
|---|---|---|---|---|
| Open-Meteo weather | weather | 32 | 0.102 | Smooth hourly diurnal temperature cycle |
| Open-Meteo air quality | air_quality | 32 | 0.442 | Pollutant variation with short spikes |
| NASA POWER meteorology | weather_energy | 112 | 0.156 | Smooth exogenous meteorology over several days |
| USGS Potomac water | hydrology | 275 | 0.066 | High-frequency river discharge with slow physical variation |
| NOAA CO-OPS water level | ocean | 240 | 0.551 | Sub-hourly tidal oscillation with values around zero |
| NOAA NDBC buoy | ocean | 76 | 0.092 | Marine wave-height fluctuations with meteorological covariates |
| Model | BTC | PM2.5 | Quake | Potomac | Water | Wave | T2M | KSFO | Temp2m | Wiki |
|---|---|---|---|---|---|---|---|---|---|---|
| Chronos-2 | 483.614 | 11.420 | 2.830 | 19.675 | 0.318 | 0.892 | 1.293 | 1.078 | 1.074 | 8.420 |
| TiRex | 497.749 | 10.843 | 2.882 | 16.958 | 0.339 | 0.899 | 1.329 | 1.003 | 1.025 | 9.889 |
| TimesFM-2.5 | 485.407 | 11.156 | 2.812 | 17.502 | 0.234 | 0.844 | 1.332 | 1.060 | 0.988 | 8.711 |
| Toto-1.0 | 1.162e+03 | 40.693 | 5.314 | 58.600 | 0.539 | 1.093 | 1.578 | 1.208 | 1.835 | 96.250 |
| Moirai-2.0 | 569.016 | 19.226 | 3.619 | 24.663 | 0.361 | 0.308 | 0.909 | 0.568 | 1.511 | 13.782 |
| Chronos-Bolt | 802.832 | 20.359 | 3.917 | 28.495 | 0.634 | 0.299 | 0.943 | 0.578 | 1.630 | 33.431 |
| Model | BTC | PM2.5 | Quake | Potomac | Water | Wave | T2M | KSFO | Temp2m | Wiki |
|---|---|---|---|---|---|---|---|---|---|---|
| Chronos-2 | 0.010 | 0.329 | 0.565 | 0.009 | 0.469 | 0.158 | 0.043 | 0.043 | 0.043 | 0.061 |
| TiRex | 0.010 | 0.315 | 0.578 | 0.007 | 0.591 | 0.164 | 0.043 | 0.038 | 0.042 | 0.057 |
| TimesFM-2.5 | 0.010 | 0.314 | 0.493 | 0.008 | 0.283 | 0.145 | 0.046 | 0.040 | 0.049 | 0.060 |
| Toto-1.0 | 0.011 | 0.333 | 0.509 | 0.010 | 0.426 | 0.171 | 0.034 | 0.031 | 0.040 | 0.210 |
| Moirai-2.0 | 0.008 | 0.341 | 0.483 | 0.009 | 0.437 | 0.178 | 0.031 | 0.031 | 0.045 | 0.046 |
| Chronos-Bolt | 0.011 | 0.364 | 0.546 | 0.010 | 0.722 | 0.176 | 0.030 | 0.031 | 0.045 | 0.134 |
| Model | BTC | PM2.5 | Quake | Potomac | Water | Wave | T2M | KSFO | Temp2m | Wiki |
|---|---|---|---|---|---|---|---|---|---|---|
| Chronos-2 | 0.112 | 0.445 | 0.345 | 0.139 | 0.166 | 0.445 | 0.059 | 0.438 | 0.092 | 0.122 |
| TiRex | 0.118 | 0.436 | 0.347 | 0.139 | 0.174 | 0.428 | 0.056 | 0.408 | 0.100 | 0.118 |
| TimesFM-2.5 | 0.136 | 0.518 | 0.481 | 0.172 | 0.147 | 0.505 | 0.071 | 0.499 | 0.111 | 0.161 |
| Toto-1.0 | 0.010 | 0.245 | 0.273 | 0.010 | 0.186 | 0.128 | 0.027 | 0.027 | 0.036 | 0.132 |
| Moirai-2.0 | 0.008 | 0.260 | 0.262 | 0.008 | 0.207 | 0.124 | 0.027 | 0.028 | 0.040 | 0.050 |
| Chronos-Bolt | 0.010 | 0.272 | 0.278 | 0.010 | 0.365 | 0.129 | 0.027 | 0.028 | 0.041 | 0.111 |
| Model | BTC | PM2.5 | Quake | Potomac | Water | Wave | T2M | KSFO | Temp2m | Wiki |
|---|---|---|---|---|---|---|---|---|---|---|
| Chronos-2 | 7.329e+05 | 494.984 | 8.908 | 2.860e+03 | 0.271 | 3.756 | 1.756 | 27.049 | 1.953 | 129.300 |
| TiRex | 6.805e+05 | 463.452 | 8.575 | 2.414e+03 | 0.310 | 3.479 | 1.653 | 27.449 | 1.788 | 167.781 |
| TimesFM-2.5 | 6.407e+05 | 499.814 | 8.574 | 2.685e+03 | 0.137 | 3.345 | 1.964 | 27.191 | 1.673 | 133.699 |
| Toto-1.0 | 3.767e+06 | 8.411e+03 | 26.727 | 9.212e+03 | 0.653 | 7.889 | 7.376 | 3.933 | 6.619 | 8.228e+03 |
| Moirai-2.0 | 4.540e+05 | 185.713 | 5.250 | 2.734e+03 | 0.192 | 0.088 | 0.375 | 0.737 | 1.538 | 64.521 |
| Chronos-Bolt | 6.818e+05 | 169.701 | 5.282 | 3.085e+03 | 0.358 | 0.052 | 1.235 | 0.981 | 2.238 | 238.712 |
| Model | BTC | PM2.5 | Quake | Potomac | Water | Wave | T2M | KSFO | Temp2m | Wiki |
|---|---|---|---|---|---|---|---|---|---|---|
| Chronos-2 | 0.560 | 0.588 | 0.398 | 0.224 | -0.033 | -0.500 | -0.138 | -0.025 | 0.527 | 0.704 |
| TiRex | 0.565 | 0.545 | 0.429 | 0.242 | -0.010 | -0.504 | 0.144 | -0.016 | 0.547 | 0.873 |
| TimesFM-2.5 | 0.531 | 0.548 | 0.431 | 0.247 | -0.051 | -0.428 | -0.002 | -0.034 | 0.585 | 0.479 |
| Toto-1.0 | -0.309 | 0.059 | -0.273 | 0.072 | 0.022 | -0.085 | 0.344 | 0.123 | 0.022 | 1.000 |
| Moirai-2.0 | -0.355 | -0.013 | -0.351 | 0.132 | -0.028 | -0.639 | -0.048 | -0.195 | -0.385 | -1.000 |
| Chronos-Bolt | 0.090 | 0.307 | -0.371 | 0.151 | 0.014 | -0.098 | -0.048 | -0.143 | -0.429 | 1.000 |
| Metric | Chr2 | TiRex | TFM | Toto1 | Moi2 | ChrB | TabPFN | Sundial | ARIMA | ETS | MovAvg | SNaive |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rank (RMSE) | 3.80 | 4.00 | 3.30 | 10.70 | 4.70 | 7.10 | 5.80 | 6.40 | 7.45 | 8.00 | 7.75 | 9.00 |
| Win Rate (RMSE) | 0.745 | 0.727 | 0.791 | 0.118 | 0.664 | 0.445 | 0.564 | 0.509 | 0.414 | 0.364 | 0.386 | 0.273 |
| Elo (RMSE) | 1225 | 1194 | 1254 | 637 | 1218 | 947 | 1161 | 1070 | 834 | 789 | 867 | 804 |
| Rank (MAPE) | 4.90 | 4.30 | 3.85 | 5.05 | 3.70 | 6.15 | 5.10 | 6.45 | 8.70 | 9.80 | 9.65 | 10.35 |
| Win Rate (MAPE) | 0.645 | 0.700 | 0.741 | 0.632 | 0.755 | 0.532 | 0.627 | 0.505 | 0.300 | 0.200 | 0.214 | 0.150 |
| Elo (MAPE) | 1163 | 1251 | 1139 | 1055 | 1253 | 1064 | 1177 | 998 | 846 | 650 | 739 | 666 |
| Group | Metric | Chr2 | TiRex | TFM | Toto1 | Moi2 | ChrB | TabPFN | Sundial | ARIMA | ETS | MovAvg | SNaive |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Air Quality | Rank (RMSE) | 3.00 | 1.00 | 2.00 | 12.00 | 9.00 | 11.00 | 10.00 | 8.00 | 4.00 | 7.00 | 5.00 | 6.00 |
| Win Rate (RMSE) | 0.818 | 1.000 | 0.909 | 0.000 | 0.273 | 0.091 | 0.182 | 0.364 | 0.727 | 0.455 | 0.636 | 0.545 | |
| Elo (RMSE) | 1451 | 1786 | 1601 | 218 | 684 | 397 | 548 | 807 | 1326 | 931 | 1191 | 1059 | |
| Rank (MAPE) | 4.00 | 3.00 | 2.00 | 5.00 | 6.00 | 8.00 | 7.00 | 1.00 | 9.00 | 12.00 | 10.00 | 11.00 | |
| Win Rate (MAPE) | 0.727 | 0.818 | 0.909 | 0.636 | 0.545 | 0.364 | 0.455 | 1.000 | 0.273 | 0.000 | 0.182 | 0.091 | |
| Elo (MAPE) | 1312 | 1438 | 1588 | 1192 | 1068 | 817 | 950 | 1783 | 695 | 206 | 553 | 397 |
| Group | Metric | Chr2 | TiRex | TFM | Toto1 | Moi2 | ChrB | TabPFN | Sundial | ARIMA | ETS | MovAvg | SNaive |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 6min | Rank (RMSE) | 3.00 | 4.00 | 1.00 | 7.00 | 5.00 | 8.00 | 6.00 | 2.00 | 9.50 | 12.00 | 9.50 | 11.00 |
| Win Rate (RMSE) | 0.818 | 0.727 | 1.000 | 0.455 | 0.636 | 0.364 | 0.545 | 0.909 | 0.227 | 0.000 | 0.227 | 0.091 | |
| Elo (RMSE) | 1436 | 1310 | 1780 | 944 | 1186 | 820 | 1062 | 1602 | 626 | 208 | 625 | 400 | |
| Rank (MAPE) | 4.00 | 6.00 | 1.00 | 2.00 | 3.00 | 8.00 | 5.00 | 7.00 | 10.00 | 9.00 | 11.00 | 12.00 | |
| Win Rate (MAPE) | 0.727 | 0.545 | 1.000 | 0.909 | 0.818 | 0.364 | 0.636 | 0.455 | 0.182 | 0.273 | 0.091 | 0.000 | |
| Elo (MAPE) | 1310 | 1068 | 1783 | 1599 | 1446 | 817 | 1182 | 947 | 549 | 692 | 399 | 206 |
| Pred. length | Metric | Chr2 | TiRex | TFM | Toto1 | Moi | Bolt | TabPFN | Sundial | ARIMA | ETS | MovAvg | SNaive |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | Rank (RMSE) | 1 | 3 | 2 | 12 | 4 | 7 | 5 | 6 | 10 | 9 | 8 | 11 |
| Rank (MAPE) | 3 | 2 | 5 | 8 | 1 | 7 | 4 | 6 | 9 | 11 | 10 | 12 | |
| Rank (CRPS) | 6 | 5 | 8 | 7 | 2 | 4 | 3 | 1 | 9 | 11 | 10 | 12 | |
| 24 | Rank (RMSE) | 2 | 3 | 1 | 12 | 4 | 6 | 5 | 9 | 7 | 8 | 10 | 11 |
| Rank (MAPE) | 5 | 4 | 6 | 2 | 1 | 8 | 3 | 7 | 10 | 9 | 11 | 12 | |
| Rank (CRPS) | 7 | 6 | 9 | 2 | 1 | 4 | 5 | 3 | 8 | 10 | 12 | 11 |
Forecasting Benchmarks
Forecasting Benchmarks are datasets and evaluation protocols for comparing predictions of future time-series values, events, and outcomes.
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