Timestral

1 Introduction

• Time series foundation models forecast across datasets and domains without retraining, providing a shared alternative to fitting a separate model for each forecasting problem.Recent advances have expanded accuracy, scaling, multivariate forecasting, and covariate support.Source: §1 · p. 1
• Timestral-209M sets a state of the art across GIFT-Eval, TIME, and fev-bench, and all four sizes lie on the Pareto front across the six panels.Timestral-123M also outperforms every other model shown, including models with billions of parameters.Source: §1 · p. 2, Figure 1 · p. 2
• Decoupled Horizon Forecasting separates prediction tokens from causal context, preserving observed values for later forecasts while allowing horizon sampling independent of context masking.The training recipe also supports multiple supervised forecast blocks within one sequence.Source: §1 · p. 3
• Role-aware covariate conditioning integrates known-future information while preserving target causality.Known-future covariates must be accessible to forecasts while future target values remain hidden.Source: §1 · pp. 2–3
• Timestral uses a two-stage pipeline: pretraining on a diverse synthetic corpus, followed by post-training on real and synthetic data with extended context.Its four model sizes range from 5M to 209M parameters and share an architecture and training recipe.Source: §1 · pp. 2–3

2.1 Time Series Foundation Models as Prior-Data Fitted Networks

• Timestral is pretrained exclusively on synthetic data, whose generators define a prior over processes, then post-trained on real and synthetic data.The report describes synthetic data as a growing part of TSFM training and cites models trained exclusively on synthetic data.Source: §2.1 · p. 3
• PFNs learn to approximate the posterior predictive distribution by predicting held-out values from observed data; in time-series PFNs, the network infers plausible processes from context in one forward pass.With negative log-likelihood training, the optimal prediction is the posterior predictive distribution.Source: §2.1 · pp. 3–4
• A TSFM’s training data defines its prior over processes, shaping forecast uncertainty: too much unpredictable variability widens forecasts, while too little makes them overconfident.With pinball loss, models learn quantiles rather than the full posterior predictive distribution.Source: §2.1 · p. 4

2.2 Time Series Foundation Model Architectures

• Patch-based models map consecutive time steps into tokens; multivariate forecasting lets target variates depend on one another, while covariates supply historical or known-future inputs.Toto-2.0 and Chronos-2 use cross-variate attention, and Chronos-2 supports both past-only and known-future covariates.Source: §2.2 · p. 4
• Bidirectional models exchange information across context and prediction positions, whereas causal models reuse shared history to forecast from each position but extend horizons autoregressively.Autoregressive sampling adds computational cost, and feeding predictions back can compound errors.Source: §2.2 · pp. 4–5
• Contiguous Patch Masking trains multi-patch forecasts by masking consecutive inputs, but those masked observations are unavailable as context for later forecasts in the same sequence.DHF separates horizon sampling from context masking while retaining shared causal context computation.Source: §2.2 · pp. 5–6

3.1 Temporal Modelling via Decoupled Horizon Forecasting

• DHF separates causal context tokens from prediction tokens, allowing forecasts to use context without changing it.Each prediction token attends to context before its forecast block and to preceding and current prediction tokens in that block; context tokens never attend to prediction tokens.Source: §3 · p. 6, §3.1 · p. 7
• Forecast blocks of sampled lengths train multiple forecast distances while sharing context representations computed once per sequence.Unlike context masking, DHF keeps observed patches available to later forecasts; it also allows forecast-distance sampling and missing-data augmentation to be controlled independently, at the cost of roughly doubling training tokens.Source: §3.1 · pp. 7–8
• At inference, one forecast block produces up to 32 patches (1,024 time steps) in a forward pass; longer horizons are forecast block by block.For longer horizons, each block is conditioned on the predicted medians of previous blocks.Source: §3.1 · p. 8

3.2 Multivariate and Covariate Modelling

• Target variates and past-only covariates are processed causally, while known-future covariates expose values across the forecast horizon.Variate attention lets targets exchange information and receive covariate information, while known-future covariates attend only to each other to prevent future information leakage.Source: Figure 4 · p. 6, §3.2 · p. 8

3.3 Architecture

• The architecture embeds 32-step patches and uses a Transformer backbone with RMSNorm, SwiGLU layers, and variate attention in every fourth block.A two-layer residual MLP quantile head predicts 21 quantiles for each time step in a forecast patch, with positive increments preventing quantile crossing.Source: §3.3 · pp. 8–9, Table 1 · p. 9

4.1 Training Setup

• Pretraining uses exclusively synthetic data at 8,192-step context, followed by shorter post-training on real and synthetic data at 32,768-step context.Source: §4.1 · p. 9
• The synthetic corpus spans diverse univariate dynamics and multivariate dependencies, with selected variates serving as past-only or known-future covariates.It includes trends, seasonality, noise, regime changes, localized events, level shifts, and count-valued observations.Source: §4.1 · p. 9
• Training uses pinball loss without auxiliary objectives, averaging equally across 21 quantile levels and scored positions.Only observed target values within forecast horizons are scored; context representations and covariates receive no direct loss.Source: §4.1 · pp. 9–10

4.2 Forecasting Performance

• Timestral-209M ranks first among compared models on all six metrics across GIFT-Eval, TIME, and fev-bench, using one checkpoint: lowest MASE and CRPS on GIFT-Eval and TIME, and highest MASE and SQL skill scores on fev-bench.Source: §4.2 · p. 10

4.3 Inference Speed

• On 8 CPU threads, forecasts take 17–113 ms; latency grows with model size, while added threads mainly benefit larger models.From 1 to 8 threads, Timestral-209M becomes 3.1 times faster, whereas Timestral-5M is already as fast on one core.Source: §4.3 · p. 12
• Timestral-28M is 3.6 times faster than Timestral-209M, while Timestral-123M has about 0.2% higher GIFT-Eval MASE at 75% of its latency.Source: §4.3 · p. 12
• One CPU core forecasts 3.5–106 series per second, while one NVIDIA H100 forecasts 3,650–18,770 series per second.The CPU throughput range is for Timestral-209M to Timestral-5M; the H100 completes 100,000 series in 5–27 seconds.Source: §4.3 · p. 12
• Latency roughly doubles from 128 to 2,048 context steps, then grows about 9–12 times through 32,768 steps; 32 variates take 7–15 times as long as one.At 32,768 steps, a forecast takes 119 ms with Timestral-5M and 1.3 s with Timestral-209M; one target plus seven known-future covariates takes 1.7–2.0 times as long as eight targets.Source: §4.3 · p. 12, Figure 9 · p. 12

• DHF separates prediction tokens from causal context, preserving observed values as both forecast targets and context for later forecasts without masking context for longer horizons.Source: §5 · p. 13
• Role-aware attention lets prediction tokens use known-future covariates while excluding future target values and past-only covariates from forecasts.Source: §5 · p. 13
• The models are pretrained exclusively on synthetic data, then post-trained on real and synthetic data with extended context.Source: §5 · p. 13
• Timestral-209M ranks first on every reported GIFT-Eval, TIME, and fev-bench metric with one checkpoint; Timestral-123M ranks second.All four sizes lie on the accuracy-versus-size Pareto front, and accuracy improves from 123M to 209M parameters.Source: §5 · p. 13
• The conclusion proposes embedding Timestral in monitoring pipelines or combining it with language models, and using context representations for classification or anomaly detection.Source: §5 · p. 13

• The appendix presents aggregate scores for GIFT-Eval, TIME, and fev-bench, then IND-Eval results and pairwise win rates against selected competitors.Source: A Detailed Results · p. 18

• Timestral-209M ranks first on all six metrics and Timestral-123M second, ahead of every non-Timestral model in the comparison.Table 3 covers leading models included in benchmark bars or the Pareto plot at the October 15, 2026 release date.Source: §A.1 · p. 18
• GIFT-Eval and TIME use geometric-mean errors where lower is better; fev-bench reports MASE and SQL skill scores in percent, where higher is better.Table 3 marks first and second place before rounding; dashes indicate missing scores.Source: Table 3 · p. 18
• IND-Eval’s aggregate nMASE and nCRPS panels show the four Timestral sizes and eleven competitors, ordered by dataset-balanced geometric-mean error.Lower is better in both panels.Source: Figure 10 · p. 19

Benchmark

• IND-Eval comprises 187 tasks in energy, manufacturing, and transport, emphasizing finer sampling resolutions and multivariate targets.The comparison includes four Timestral sizes and eleven competitors.Source: §A.2 · p. 19

Evaluation

• All models are evaluated zero-shot under the official protocol, with context capped at 4,096 steps and aggregate scores weighting datasets equally.Task errors are divided by Seasonal Naive errors; values below one indicate lower error.Source: §A.2 · p. 19

Aggregate results

• 0.646 nMASE and 0.435 nCRPS place Timestral-209M first; these errors are about 7% lower than t0-gamma’s 0.697 nMASE and 0.469 nCRPS.Timestral-123M and Timestral-28M also outperform every non-Timestral model on both aggregate metrics.Source: §A.2 · p. 19

Method

• Pairwise win rates count lower task error as a win and exact ties as half a win, with tasks equally weighted and errors compared before rounding.The figures compare the four Timestral sizes with selected competitors.Source: §A.3 · p. 20

Pairwise results

• Timestral-209M wins a majority of tasks against every selected competitor on both metrics of each benchmark; Timestral-123M does so on all four benchmarks.The evaluations follow official protocols, with IND-Eval results produced by the authors’ own runs.Source: §A.3 · p. 20

GIFT-Eval

• GIFT-Eval win rates compare MASE and CRPS across 97 dataset–frequency–horizon configurations; rates above 50% favor the row model.CRPS uses the official nine-quantile approximation.Source: Figure 11 · p. 20

TIME

• TIME win rates compare MASE and CRPS across 98 dataset–frequency–horizon configurations, with task errors averaged over series, forecast windows, and variates.Configurations are equally weighted; rates above 50% favor the row model.Source: Figure 12 · p. 21

fev-bench

• fev-bench win rates compare MASE and SQL across 100 official tasks; SQL scales quantile loss by the context’s mean absolute seasonal error.Tasks are equally weighted, and rates above 50% favor the row model.Source: Figure 13 · p. 21

IND-Eval

• IND-Eval win rates compare nMASE and nCRPS across 187 tasks, using authors’ evaluations under the official protocol.Task win rates equally weight tasks, while aggregate errors weight datasets equally.Source: Figure 14 · p. 22