Chronos-2: A foundation model for multivariate time series forecasting
Authors: Abdul Fatir Ansari, Oleksandr Shchur, Jaris Küken, Andreas Auer, Boran Han, Pedro Mercado, Syama Sundar Rangapuram, Huibin Shen, Lorenzo Stella, Xiyuan Zhang, Mononito Goswami, Shubham Kapoor, Danielle C. Maddix, Pablo Guerron, Florian Saupe, Markus Reichstein, Tony Hu, Junming Yin, Nick Erickson, Prateek Mutalik Desai, Hao Wang, Huzefa Rangwala, George Karypis, Yuyang Wang, Michael Bohlke-Schneider
Organizations: Amazon Web Services · University of Freiburg · Amazon · Boston College · Max Planck Institute for Biogeochemistry · Rutgers University
Accurate forecasting with uncertainty quantification is critical in a variety of scientific applications ranging from epidemiology and economics to energy systems and earth sciences. Yet most forecasting models still need to be developed and trained separately for each domain-specific dataset. Time series foundation models (TSFMs) aim to remove this limitation and enable the application of the same model across domains through large-scale pretraining. However, most existing TSFMs treat each time series independently and therefore cannot model interactions among time series and external drivers. Here, we introduce Chronos-2, a foundation model for zero-shot forecasting that models the interactions between multivariate time series and heterogeneous covariates, which commonly arise in scientific applications. The model infers relationships among time series directly from historical context and generates probabilistic forecasts without task-specific treatment. Across various benchmarks, Chronos-2 achieves state-of-the-art accuracy on average by improving skill scores by 5.2 percentage points relative to the strongest baselines and increasing win rates by 10 percentage points. Chronos-2 is also computationally efficient, generating forecasts for 100 time series in under one second on a single mid-range GPU, 50x and 1000x faster end-to-end than the best task-specific point and probabilistic forecasters, respectively. In addition, we demonstrate its effectiveness in diverse scientific settings -- including infectious-disease forecasting, macroeconomic modeling, carbon-flux prediction, and runoff simulation -- where the model matches or surpasses specialized methods developed for each domain. These results show that a single pretrained model can capture structure shared across temporal systems.
Figures & tables
Figure 1: The complete Chronos-2 pipeline. (a) Architecture overview : Input time series (targets and covariates) are first normalized (scaling) and then tokenized for downstream processing. The Transformer stack alternates between time and group attention layers. The output from the Transformer stack is mapped to quantile predictions through a neural network. The figure illustrates two time series tasks, the first (in cyan ) with two targets and one known (future) covariate, and the second (in pink ) with one target and two known covariates. (b) Tokenization : Meta features are appended to the time series which indicate the position of an observation (time index) and whether it is missing (mask). Time series and meta features are split into non-overlapping patches and mapped to high-dimensional embeddings via a neural network. (c) Attention layers : Each Transformer block alternates between time and group attention layers: the time attention layer aggregates information across patches within a single time series, and the group attention layer aggregates information across all series within a group at each patch index. The groups corresponding to the two time series tasks are highlighted in cyan and pink . A group is a flexible notion of relatedness and may correspond to a single time series, multiple series sharing a source or metadata, variates of a multivariate series, or targets along with associated covariates. The group attention layer enables the model to infer relationships between different time series in the group based on the available context at inference time (in-context learning).
Figure 2: Generation of multivariate synthetic training data . We generate multivariate synthetic time series by applying random transformation functions to time series sampled from univariate generators. Univariate generators produce diverse temporal patterns to serve as the building blocks for multivariate data. These include: (a.1) KernelSynth ( Ansari et al., 2024a ) , which draws samples from Gaussian processes defined by the random composition of basic kernels (e.g., linear, periodic); (a.2) Trend-Seasonality-Irregularity (TSI), which stochastically combines structural components; and parametric simulations using random (a.3) Autoregressive (AR) and (a.4) Exponential Smoothing (ETS) processes. (b.1) Instantaneous transformations impose coupling between variables without time delays. A mixing function transforms univariate samples at each time step. We employ (b.2) random linear operators (e.g., random dense, sparse, sign or aggregation matrices) and (b.3) non-linear mappings via random Multi-Layer Perceptrons (MLPs) to simulate complex static dependencies. (c.1) Sequential transformations introduce time-delayed relationships between time series. A random function maps a look-back window of univariate series to multivariate outputs. We generate (c.2) linear lead-lag relationships via a Temporal Causal Model, which samples sparse directed edges across time and variates (simulating Vector Autoregression), while (c.3) non-linear dynamic correlations are introduced via random Recurrent Neural Networks (RNNs).
Figure 3: Evaluation of Chronos-2 on time series forecasting benchmarks ( best viewed in color on a screen ). Performance is evaluated using the Mean Absolute Scaled Error (MASE) and Scaled/Weighted Quantile Loss (SQL/WQL) for point and probabilistic forecasts, respectively. The Win Rate measures the proportion of pairwise comparisons where a model outperforms competitors, while the Skill Score reflects the average percentage improvement over a Seasonal Naive baseline. Dark purple bars denote Chronos-2 in univariate mode (group attention disabled); light purple segments highlight the performance gain attributed to in-context learning (ICL) via group attention. Error bars indicate 95% confidence intervals obtained through bootstrapping. (a) Results on fev-bench ( n=100 tasks), a rigorous benchmark where 68 tasks involve multivariate dependencies. Chronos-2 outperforms all baselines, including statistical ensembles, tree-based methods, task-specific deep learning models, and existing foundation models, while maintaining fast inference speed; Wilcoxon signed-rank test p<10−6 against all baselines (see Tables S4 and S5 in the Appendix for results in tabular format and Table S6 for the p -values). (b) Results on Chronos-Bench-II ( n=27 tasks) and GIFT-Eval ( n=97 tasks), which focus primarily on univariate forecasting. Chronos-2 outperforms or ties state-of-the-art methods; notably, enabling ICL yields performance improvements even in these univariate settings by retrieving patterns across related series. n.s. indicates that the performance difference relative to Chronos-2 is not statistically significant ( p≥0.05 ) based on the Wilcoxon signed-rank test; see Tables S7 , S8 , S10 and S11 in the Appendix for results in tabular format and Tables S9 and S12 for the p -values.
Figure 4: Qualitative analysis of in-context learning ( best viewed in color on a screen ). Probabilistic forecasts show the 10% to 90% quantile interval; bar charts show SQL forecast errors per time step. (a) Retail sales forecasting: univariate inference versus in-context learning with covariates including promotions, customer traffic, and holiday indicators. Covariates are shown in the lower panels. (b) Regime change: store closure at different positions relative to the forecast horizon. The top and bottom rows show the same series with different forecast origins, so that the closure falls within the forecast horizon (top) or entirely within the historical context (bottom). (c) Scenario analysis with simulated future covariates: promotion intensity (top four panels) and customer count trajectories (bottom panel) varied across hypothetical trajectories. (d) Energy load forecasting: univariate, past-only covariates, and full covariates (air temperature, dew temperature, sea-level pressure). The three rows show progressively more covariate information available to the model.
Figure 5: Zero-shot forecasting of complex human-centric systems. (a) Forecasting incidence of Acute Respiratory Infection (ARI) and Influenza-Like Illness (ILI) across 31 European countries. Performance is evaluated using the Weighted Interval Score (WIS) relative to a simple quantile baseline provided by RespiCast ( European Centre for Disease Prevention and Control, 2026 ) , calculated as log2(WISbaseline/WISmodel) ; values greater than 0 indicate improvement over the baseline. Plots show the median relative WIS (solid lines) and 95% confidence intervals (shaded bands) over 67 rolling evaluation windows (Oct 2024–Jan 2026). In univariate mode (U), Chronos-2 is competitive at short horizons (1 week) against the operational RespiCast Hub-Ensemble (a consensus of mechanistic and statistical models). At longer horizons ( >1 week), Chronos-2 significantly outperforms the ensemble, with in-context learning yielding further gains by exploiting cross-country correlations (Wilcoxon signed-rank test p<0.001 ). (b) Joint forecasting of German Consumer Price Index (CPI) components (2021–2025). Performance is measured by the Root Mean Squared Error (RMSE) relative to a Seasonal Naive baseline, log2(RMSEbaseline/RMSEmodel) . While univariate inference (U) performs comparably to robust statistical baselines, enabling in-context learning significantly improves accuracy by leveraging shared structural patterns within CPI groups. Pairwise comparisons (right) confirm that Chronos-2 outperforms the strongest baseline (AutoETS) on the majority of item-window pairs (Wilcoxon signed-rank test p<0.001 for both 3-month and 12-month horizons).
Figure 6: Ecosystem carbon and energy flux prediction with Chronos-2. We evaluate the performance of Chronos-2 on daily eddy-covariance targets from the FLUXNET collection ( Pastorello et al., 2020 ) . (a) Comparison of the distribution of site-level RMSE across 65 sites for net ecosystem exchange (NEE), latent heat flux (LE), and sensible heat flux (H) over the June–August 2020 evaluation window between supervised regression baselines (XGBoost, trained either as a single pooled model across sites or as site-specific models) and Chronos-2 in zero-shot mode. Box plots show the median (center line), interquartile range (box limits), and 1.5 × interquartile range (whiskers); points denote outliers. (b) Representative summer time series at the Monte Bondone site in Italy (IT-MBo), showing observed fluxes (black) and Chronos-2 predictions from the meteorological covariates with 10–90% prediction intervals (red shaded); the corresponding covariates (TA, SW_IN and VPD) are shown below. (c) Rolling one-month-ahead forecasting over the full year 2020. For each evaluation month, models condition on the preceding 12 months of context and predict the subsequent month (step size: 1 month). Bars report normalized RMSE (RMSE divided by the target standard deviation) stratified by prediction month for Chronos-2 and XGBoost, highlighting seasonal variations in predictability across NEE, LE, and H.
Figure 7: Rainfall-runoff simulation using Chronos-2. Performance is evaluated using the Nash–Sutcliffe Efficiency (NSE), where a score of 1.0 represents perfect correspondence between simulated and observed discharge. (a) Top: Distribution of NSE scores across 1,582 catchments in the CAMELS-DE dataset. The zero-shot Chronos-2 (ICL) model achieves a median NSE of 0.68, significantly outperforming univariate inference (Chronos-2 (U), NSE=0.15) by leveraging meteorological covariates. While the domain-specific LSTM ensemble achieves higher performance (NSE=0.90), fine-tuning Chronos-2 (FT) bridges this gap, matching state-of-the-art performance without ensembling, access to static attributes, or training on the NSE metric. Box plots show the median (center line), interquartile range (box limits), and 1.5 × interquartile range (whiskers). Bottom: Exceedance probability curves showing the cumulative proportion of basins (y-axis) achieving an NSE score greater than or equal to a specific threshold (x-axis). The fine-tuned model closely tracks the reliability profile of the LSTM ensemble. (b) Hydrograph for a single catchment (DE110180) over one year. The zero-shot prediction (top) captures the relationship between rainfall and runoff but exhibits high uncertainty (shaded region denotes 10-90% prediction interval). Fine-tuning (bottom) tightens the predictive distribution, accurately modeling the discharge.
Figure 8: Hierarchical forecasting with Chronos-2. (a) Mean and maximum coherence error on the Tourism-Q and Tourism-M datasets for Chronos-2 (U) and Chronos-2 (ICL). Enabling ICL reduces the coherence error on both datasets. (b) Root-level forecasts on Tourism-Q. Solid red line shows the direct forecast generated by the respective models for the root level, while the dashed blue line shows the bottom-up aggregated forecasts. The shaded region shows the coherence gap. Chronos-2 (ICL) produces a narrower gap than Chronos-2 (U) indicating that group attention implicitly learns the aggregation structure. (c) Distribution of per-series scaled quantile loss (SQL) with bottom-up reconciliation on Tourism-Q (left) and Tourism-M (right). Chronos-2 (ICL) achieves the lowest median SQL on both datasets (0.56 and 0.60, respectively), outperforming the end-to-end HierE2E model trained specifically for hierarchical coherence as well as ETS and ARIMA statistical baselines. Methods are ordered by median SQL.
Appendix figures & tables19 assets
Supplementary material from the paper’s appendix.
Appendix
fev-bench
Chronos-Bench-II
GIFT-Eval
Model
SQL ↑
MASE ↑
WQL ↑
MASE ↑
WQL ↑
MASE ↑
Training data composition
Chronos-2 (Stage-1)
0.469
0.352
0.458
0.250
0.501
0.281
Real data only
0.419
0.289
0.431
0.233
0.484
0.258
Synthetic data only
0.449
0.329
0.453
0.246
0.491
0.259
No sequential multivariate data
0.459
0.339
0.447
0.232
0.493
0.268
Appendix
Table 1: Ablation study on training data composition, group attention, and long-context training. All metrics are reported as skill scores (higher is better). For each ablation group, the reference model is shown in bold. Training data ablations and the group attention ablation use the first stage (Stage-1) training protocol. † Equivalent to the Stage-1 checkpoint.
Dataset Name
Frequencies
# Time Series
Domain
Source
Electricity
15min, 1H, 1W, 1D
370
Energy
Godahewa et al. (2021)
KDD Cup (2018)
1H, 1D
270
Nature
Godahewa et al. (2021)
M4 (Daily)
1D
4227
Various
Makridakis et al. (2020)
M4 (Hourly)
1H
414
Various
Makridakis et al. (2020)
M4 (Monthly)
1M
48000
Various
Makridakis et al. (2020)
M4 (Weekly)
1W
359
Various
Makridakis et al. (2020)
Appendix
Table S1: Real univariate datasets used for pretraining Chronos-2.
Task Type
Group IDs g
Future Inputs W
Univariate Forecasting ( 3 independent series )
g=(1,2,3)
W=∗∗∗………∗∗∗∈R3×H
Multivariate Forecasting ( 3 targets )
g=(1,1,1)
W=∗∗∗………∗∗∗∈R3×H
Forecasting with Covariates ( 1 target, 1 past-only covariate, 2 known covariates )
g=(1,1,1,1)
W=∗∗xT+1,3xT+1,4…………∗∗xT+H,3xT+H,4∈R4×H
Appendix
Table S2: Diverse forecasting tasks can be solved by specifying group IDs and future inputs appropriately. Here, g and W denote the group IDs and future values provided to the model. Future inputs for targets and past-only covariates are masked as missing values, denoted as ∗ . The examples use fixed numbers of variates for clarity, but Chronos-2 can handle arbitrary dimensions.
Chronos-2
Chronos-Bolt
Chronos
Input Type
Patches
Patches
Individual Observations
Output Type
Multi-step Quantile Forecast
Multi-step Quantile Forecast
Autoregressive Sampling
Loss Function
Quantile Loss
Quantile Loss
Cross Entropy Loss
Univariate Forecasting
✓
✓
✓
Cross Learning
✓
–
–
Multivariate Forecasting
✓
–
–
Appendix
Table S3: Comparison of Chronos-2 with previous versions of the Chronos family.
Model
Skill Score (%)
Skill Score 95% CI
Avg. Win Rate (%)
Win Rate 95% CI
Median runtime (s)
#Failures
Chronos-2
35.5
(31.6, 39.5)
88.8
(86.2, 91.2)
0.8
0
TiRex
30.0
(26.4, 33.8)
79.8
(76.8, 82.8)
0.2
0
TimesFM-2.5
30.3
(26.7, 34.2)
79.2
(75.5, 82.8)
1.9
0
Toto-1.0
28.2
(23.9, 32.7)
69.8
(64.9, 74.3)
22.1
0
Moirai-2.0
27.3
(23.3, 31.3)
65.5
(61.1, 69.2)
0.3
0
Chronos-Bolt
26.5
(22.5, 30.5)
65.1
(61.2, 68.7)
0.2
0
Appendix
Table S4: Point forecasting results on fev-bench . The average win rate and skill score are computed with respect to the mean absolute scaled error (MASE) metric. Higher values are better for both. Scores for models with failures on specific tasks were imputed with the baseline (Seasonal Naive) score, as described in Shchur et al. (2025) .
Model
Skill Score (%)
Skill Score 95% CI
Avg. Win Rate (%)
Win Rate 95% CI
Median runtime (s)
#Failures
Chronos-2
47.3
(42.9, 52.2)
92.4
(90.5, 94.1)
0.8
0
TiRex
42.6
(38.1, 47.5)
85.2
(82.6, 87.6)
0.2
0
TimesFM-2.5
42.3
(37.9, 47.4)
81.5
(78.2, 84.6)
1.9
0
Toto-1.0
40.7
(35.8, 46.3)
75.1
(71.1, 78.6)
22.1
0
Moirai-2.0
39.3
(34.4, 44.5)
70.2
(66.6, 73.1)
0.3
0
Chronos-Bolt
38.9
(34.2, 44.1)
69.8
(66.9, 72.5)
0.2
0
Appendix
Table S5: Probabilistic forecasting results on fev-bench . The average win rate and skill score are computed with respect to the scaled quantile loss (SQL) metric. Higher values are better for both. Scores for models with failures on specific tasks were imputed with the baseline (Seasonal Naive) score, as described in Shchur et al. (2025) .
Table S6: Holm-Šidák (HS) adjusted p values of the one-sided Wilcoxon signed rank test comparing Chronos-2 against all baselines on fev-bench . *** p<0.001 , ** p<0.01 , * p<0.05 .
Model
Skill Score (%)
Skill Score 95% CI
Avg. Win Rate (%)
Win Rate 95% CI
Chronos-2
26.5
(19.9, 33.7)
79.5
(70.6, 87.7)
TimesFM-2.5
23.3
(17.4, 29.8)
72.1
(64.7, 79.5)
TiRex
22.2
(15.7, 28.9)
67.7
(60.5, 73.3)
Stat-Ens
19.6
(12.4, 27.4)
64.9
(52.8, 76.8)
Toto-1.0
22.3
(16.2, 28.5)
60.7
(51.9, 70.6)
DeepAR
18.4
(12.0, 24.9)
57.5
(46.4, 67.7)
Appendix
Table S7: Point forecasting results on Chronos-Bench-II . The average win rate and skill score are computed with respect to the mean absolute scaled error (MASE) metric. Higher values are better for both. Scores for models with failures on specific tasks were imputed with the baseline (Seasonal Naive) score, as described in Ansari et al. (2024a) .
Model
Skill Score (%)
Skill Score 95% CI
Avg. Win Rate (%)
Win Rate 95% CI
Chronos-2
46.6
(36.3, 56.4)
79.5
(70.4, 87.7)
TiRex
41.7
(31.0, 52.1)
73.8
(65.9, 80.2)
TimesFM-2.5
42.4
(31.7, 52.8)
72.3
(65.7, 78.8)
Toto-1.0
41.9
(30.6, 52.4)
64.4
(55.6, 73.3)
Moirai-2.0
40.9
(28.9, 51.7)
61.0
(50.4, 71.6)
TFT
36.2
(24.9, 46.9)
57.9
(46.8, 69.3)
Appendix
Table S8: Probabilistic forecasting results on Chronos-Bench-II . The average win rate and skill score are computed with respect to the weighted quantile loss (WQL) metric. Higher values are better for both. Scores for models with failures on specific tasks were imputed with the baseline (Seasonal Naive) score, as described in Ansari et al. (2024a) .
Table S9: Holm-Šidák (HS) adjusted p values of the one-sided Wilcoxon signed rank test comparing Chronos-2 against all baselines on Chronos-Bench-II . *** p<0.001 , ** p<0.01 , * p<0.05 .
Model
Skill Score (%)
Skill Score 95% CI
Avg. Win Rate (%)
Win Rate 95% CI
Chronos-2
30.2
(26.5, 34.5)
87.8
(84.4, 90.7)
TimesFM-2.5
29.5
(25.5, 34.2)
84.4
(81.5, 87.3)
TiRex
27.6
(23.8, 31.8)
79.0
(75.1, 82.4)
Moirai-2.0
27.2
(23.3, 31.5)
74.5
(71.0, 77.8)
Toto-1.0
25.2
(21.7, 29.1)
72.9
(69.7, 76.1)
Chronos-Bolt
19.2
(11.2, 25.9)
68.6
(64.0, 73.1)
Appendix
Table S10: Point forecasting results on GIFT-Eval . The average win rate and skill score are computed with respect to the mean absolute scaled error (MASE) metric. Higher values are better for both. Scores for models with failures on specific tasks were imputed with the baseline (Seasonal Naive) score, as described in Aksu et al. (2024) .
Model
Skill Score (%)
Skill Score 95% CI
Avg. Win Rate (%)
Win Rate 95% CI
Chronos-2
51.4
(47.0, 55.3)
85.9
(82.7, 88.9)
TimesFM-2.5
51.0
(46.4, 55.3)
83.4
(79.7, 86.4)
TiRex
50.2
(45.7, 54.4)
81.6
(78.1, 84.7)
Toto-1.0
48.6
(43.9, 52.9)
76.3
(73.1, 79.4)
Moirai-2.0
48.4
(43.7, 52.8)
72.8
(69.3, 76.0)
TabPFN-TS
43.1
(37.9, 48.0)
65.2
(61.6, 68.6)
Appendix
Table S11: Probabilistic forecasting results on GIFT-Eval . The average win rate and skill score are computed with respect to the weighted quantile loss (WQL) metric. Higher values are better for both. Scores for models with failures on specific tasks were imputed with the baseline (Seasonal Naive) score, as described in Aksu et al. (2024) .
Table S12: Holm-Šidák (HS) adjusted p values of the one-sided Wilcoxon signed rank test comparing Chronos-2 against all baselines on GIFT-Eval . *** p<0.001 , ** p<0.01 , * p<0.05 .
Figure S1: Calibration of probabilistic forecasts across benchmarks ( best viewed in color on a screen ). Comparison of Chronos-2 against baselines that support extreme quantiles on three central prediction intervals: 90% [0.05,0.95] , 95% [0.025,0.975] , and 98% [0.01,0.99] . Left panels show the geometric mean of the Weighted Interval Score (WIS), a strictly proper scoring rule that jointly assesses calibration and sharpness, relative to the Seasonal Naive baseline; lower values indicate better performance. Right panels show the Mean Absolute Coverage Error (MACE), which measures the discrepancy between nominal and empirical interval coverage; lower values indicate better calibration. Results are shown for (a) fev-bench , (b) Chronos-Bench-II , and (c) GIFT-Eval . Chronos-2 achieves the best calibration on 23 out of 24 metric-interval pairs across the three benchmarks.
Task
Domain
Freq.
H
W
Med. length
# series
# targets
# past cov.
# known cov.
# static cov.
Australian Tourism
econ
Q
8
2
36
89
1
0
0
0
BizITObs - L2C
cloud
5T
288
20
31,968
1
7
0
0
0
BizITObs - L2C
cloud
H
24
20
2,664
1
7
0
0
0
BOOMLET - 1062
cloud
5T
288
20
16,384
1
21
0
0
0
BOOMLET - 1209
cloud
5T
288
20
16,384
1
53
0
0
0
BOOMLET - 1225
cloud
T
60
20
16,384
1
49
0
0
0
Appendix
Table S13: Task statistics for fev-bench (Part 1/2). H denotes the forecast horizon, W the number of rolling evaluation windows. Median length refers to the median number of time steps across series in a task.
Task
Domain
Freq.
H
W
Med. length
# series
# targets
# past cov.
# known cov.
# static cov.
Hierarchical Sales
retail
D
28
10
1,825
118
1
0
0
0
Hierarchical Sales
retail
W
13
10
260
118
1
0
0
0
Hospital
healthcare
M
12
4
84
767
1
0
0
0
Hospital Admissions
healthcare
D
28
20
1,731
8
1
0
0
0
Hospital Admissions
healthcare
W
13
16
246
8
1
0
0
0
Jena Weather
nature
10T
144
20
52,704
1
21
0
0
0
Appendix
Table S14: Task statistics for fev-bench (Part 2/2).
Task
Domain
Freq.
H
W
Avg. length
# series
# targets
Australian Electricity
energy
30T
48
1
231052
5
1
CIF 2016
banking
M
12
1
98
72
1
Car Parts
retail
M
12
1
51
2674
1
Covid Deaths
healthcare
D
30
1
212
266
1
Dominick
retail
D
8
1
296
100014
1
ERCOT Load
energy
H
24
1
154854
8
1
Appendix
Table S15: Task statistics for Chronos-Bench-II . H denotes the forecast horizon, W the number of rolling evaluation windows.
Task
Domain
Freq.
H
W
Avg. length
# series
# targets
Jena Weather (10T, S)
Nature
10T
48
20
52,704
1
21
Jena Weather (10T, M)
Nature
10T
480
11
52,704
1
21
Jena Weather (10T, L)
Nature
10T
720
8
52,704
1
21
Jena Weather (H, S)
Nature
H
48
19
8,784
1
21
Jena Weather (H, M)
Nature
H
480
2
8,784
1
21
Jena Weather (H, L)
Nature
H
720
2
8,784
1
21
Appendix
Table S16: Task statistics for GIFT-Eval (Part 1/2). H denotes the forecast horizon, W the number of rolling evaluation windows. S/M/L denote short/medium/long-term prediction horizons.
Task
Domain
Freq.
H
W
Avg. length
# series
# targets
Loop Seattle (H, L)
Transport
H
720
2
8,760
323
1
Loop Seattle (D, S)
Transport
D
30
2
365
323
1
SZ-Taxi (15T, S)
Transport
15T
48
7
2,976
156
1
SZ-Taxi (15T, M)
Transport
15T
480
1
2,976
156
1
SZ-Taxi (15T, L)
Transport
15T
720
1
2,976
156
1
SZ-Taxi (H, S)
Transport
H
48
2
744
156
1
Appendix
Table S17: Task statistics for GIFT-Eval (Part 2/2).
Despite the success of Time Series Foundation Models (TSFMs) on broad benchmarks, their ability to internalize basic temporal logic, especially in settings supported by exogenous covariates, remains under-examined. We introduce SimpleTimeBench, a diagnostic univariate and multivariate "unit test" suite for primitives such as monotonic trends, periodic signals and leading indicator covariates, scenarios where near-perfect forecasts should be trivial. Surprisingly, prominent multivariate TSFMs (Chronos-2, Moirai and Toto) frequently produce suboptimal zero-shot forecasts for these inputs. While fine-tuning Chronos-2 improves its behaviour on specific tasks, we show that this adaptation degrades performance on other fundamental patterns rather than enhancing its generalizable foundational capabilities. This reveals a gap between pre-training scale and basic temporal reasoning, suggesting that current TSFMs could potentially lack the inductive biases needed to capture simple predictable functions. We further demonstrate that these failures are not merely synthetic curiosities: they persist in real-world sensor forecasting, where TSFMs consistently underutilize leading indicators available in observed covariates. This inability to capture simple relationships limits the practical utility and reliability of current multivariate models.
Using Chronos-2, an open-source time-series foundation model, we evaluate pretrained time-series models for economic and financial forecasting with an emphasis on whether multivariate (MV) inputs improve accuracy relative to univariate (UV) baselines. The study covers two panels -- the Magnificent-7 equities and U.S. Treasury interest rates -- as well as a combined panel, using rolling monthly evaluations from 2000--2025. We vary input window lengths and forecast horizons and report RMSE and MAPE. Across datasets, MV forecasts consistently outperform UV forecasts, with especially strong gains for interest rates and meaningful improvements for equities. Series-level comparisons show MV improvements in every case, and error dispersion is generally lower under MV inputs. We also provide parameter-heatmap and time-series visualizations. However, mixing time series across equity and interest rate markets reduces forecast accuracy, indicating that adding noisy context degrades model performance. Overall, the results indicate that foundation models can leverage cross-series information to improve forecast accuracy in finance, and that the benefits are strongest when related series are modeled jointly under disciplined rolling protocols. Other than using an open-source foundation model, this paper also showcases how AI may be used for financial research.
We introduce Timer-M1, a pretrained multivariate time series foundation model that learns with primitives for zero-shot forecasting. Across domains, time series share elementary temporal and relational patterns, termed primitives, yet differ in how these primitives manifest and evolve across different contexts. Despite progress in zero-shot and task-general forecasting, existing foundation models may still struggle to generalize to complex real-world scenarios. To this end, we develop a primitive-based data synthesis and pretraining pipeline. The synthesis pipeline generates series with temporal primitives shared across domains and then assembles real and generated series into multivariate samples using relational primitives. Afterwards, samples are organized into episodes by assigning distinct channel roles as target variates, past-only covariates, and known-future covariates, ensuring that the model is optimized on predictable variates using available exogenous information. Technically, Timer-M1 further adapts gated two-dimensional Transformer blocks that dynamically allocate cross-variate attention across layers. Across three large-scale forecasting benchmarks, Timer-M1 ranks first on both FEV and TIME and second on GIFT-Eval among most recent time series foundation models. These results support effective primitive-based pretraining as a route to robust general forecasting technique across domains and task settings.
Haoran Zhang, Haixuan Liu, Xingjian Su +5
School of Software, BNRist, Tsinghua University · ByteDance, Beijing, China