Zero-Shot Forecasting: What Time-Series Foundation Models Actually Learned

TiRex has 35 million parameters, which is roughly one four-thousandth of a frontier language model, and it has never seen your data. Its authors report it setting the state of the art in zero-shot forecasting on the GiftEval and Chronos-ZS benchmarks, ahead of substantially larger models including TabPFN-TS, Chronos-Bolt, TimesFM and Moirai (Auer et al., 2025, TiRex, NeurIPS 2025, arXiv:2505.23719). You can point it at a series it has never encountered, hand it no training loop, no hyperparameters and no validation split, and get back calibrated quantiles in a single forward pass.

Every part of that sentence is true, and the conclusion most teams draw from it is wrong. The conclusion is usually "forecasting is solved, delete the pipeline." What the result actually shows is narrower and more interesting: a model trained on a large enough corpus of series learns a very good prior over the shapes univariate series take, and that prior is worth the most in exactly the situations where you have the least, which are rarely the situations that carry the business value.

Why this matters: Pretrained forecasters change the economics of the long tail, where fitting a model per series was never affordable. They do not change the economics of the head, where covariates, hierarchy and decision structure dominate. Knowing which regime you are in, and knowing how much of the reported benchmark advantage survives contamination auditing, is the difference between deleting the right pipeline and the wrong one.

TL;DR

• Zero-shot forecasters learned a shape prior, not domain knowledge. They interpolate between seasonal and trend patterns seen in pretraining; they cannot know that your Tuesday promotion exists.
• The strongest measured advance of 2025 was not scale. Chronos-2, at around 100M parameters, beat larger models by putting covariates and related series back into the model through in-context learning, reporting a skill score of 0.473 on fev-bench against 0.426 for TiRex and 0.407 for Toto-1.0 (Ansari, Shchur et al., 2025, arXiv:2510.15821).
• An 11M-parameter tabular model matched or slightly beat Chronos-Large, which has 65 times more parameters, by treating forecasting as regression over simple temporal features (Hoo et al., 2025, arXiv:2501.02945). Parameter count is a weak predictor of forecasting accuracy.
• Benchmark contamination is now measurable rather than theoretical. TSFMAudit audited 6 pretrained forecasters across 187 datasets and detects contamination from adaptation dynamics (arXiv:2605.26161); a separate analysis argues current benchmarks risk measuring memorisation rather than generalisation (arXiv:2510.13654).
• The M5 lesson has not been repealed. Where covariates and cross-series structure exist, a well-engineered global LightGBM is still the method to beat, and it was the first competition where pure machine learning beat every statistical benchmark and their combinations (Makridakis et al., 2022, IJF 38(4)).
• The engineering win is real and mostly operational: no per-series fitting, no retraining schedule, no cold-start special case, one artefact. That is worth a lot before a single accuracy point is counted.

At a Glance

flowchart LR
    A["Raw series<br/>any scale or frequency"] --> B["Instance scaling<br/>and patching"]
    B --> C["Pretrained backbone<br/>the shape prior"]
    C --> D["Quantile decode<br/>predictive distribution"]
    D --> E["Forecast<br/>h steps ahead"]
    F["Covariates and<br/>related series"] -->|"no channel until 2025"| C
    G["Your domain<br/>knowledge"] -.-> H["Not represented<br/>anywhere"]

    classDef blue fill:#1e40af,stroke:#3b82f6,stroke-width:1px,color:#fff
    classDef purple fill:#6d28d9,stroke:#a78bfa,stroke-width:1px,color:#fff
    classDef teal fill:#0e7490,stroke:#22d3ee,stroke-width:1px,color:#fff
    classDef rose fill:#be123c,stroke:#fb7185,stroke-width:1px,color:#fff
    classDef slate fill:#334155,stroke:#64748b,stroke-width:1px,color:#e2e8f0
    class A,F blue
    class B,C purple
    class D,E teal
    class H rose
    class G slate

The whole architecture is a compression of one claim: if you normalise scale away and chop the series into patches, what remains is a pattern that recurs across domains often enough to be learned once. Everything contested about these models lives in the two edges entering from below, the covariate channel that the first generation did not have and the domain knowledge that no generation has.

[IMAGE: Side-by-side line charts of four unrelated series after instance normalisation: hourly electricity load, weekly retail units, daily website sessions, and monthly river flow. All four are z-scored and overlaid faintly in grey behind a bold median curve. Caption: "After scale is removed, series from unrelated domains share a small number of recurring shapes. That overlap is the entire premise of pretraining."]

Before Pretrained Forecasters

Forecasting spent forty years being an estimation problem: one series, one model class, parameters estimated from that series' own past. The M competitions were the field's periodic reality check, and their verdict was consistently deflationary, with simple methods and combinations of them beating sophisticated ones.

Two competitions broke the pattern. M4 in 2018 was won by Slawek Smyl's hybrid of exponential smoothing and a recurrent network, the first time a machine learning component featured in a winner, and the organisers' broader finding was that combinations dominated individual methods across the 100,000 series. M5 in 2020 went further: every top method used LightGBM, and it was the first M competition in which all top performers were pure machine learning and beat all statistical benchmarks and their combinations (Makridakis, Spiliotis & Assimakopoulos, 2022).

What made M5 different was not the algorithm. It was that 30,490 Walmart product-store series, sharing calendars, prices and promotions, could be fitted as one model. That is the global-model insight, and pretraining is its logical extension: if pooling 30,000 related series helps, what happens if you pool billions of unrelated ones?

timeline
    title From estimation to pretraining
    2018 : M4 competition; Smyl's ES-RNN hybrid wins
         : Combinations beat individual methods across 100,000 series
    2020 : M5 competition; LightGBM sweeps the leaderboard
         : Global models with covariates beat all statistical benchmarks
    2023 : TimeGPT-1 proposes a pretrained forecasting service
         : Lag-Llama releases open decoder-only weights using lags as covariates
    2024 : Chronos tokenises scaled values for a T5 backbone
         : TimesFM patches a decoder-only model over 100B time points
         : Moirai trains on the 27B-observation LOTSA archive
         : GIFT-Eval ships a non-leaking pretraining corpus
    2025 : TiRex reaches the frontier with 35M xLSTM parameters
         : Toto and BOOM target observability data
         : Chronos-2 restores covariates through group attention
    2026 : Contamination auditing makes benchmark leakage measurable

The 2023 entries staked the claim. TimeGPT-1 argued that a single pretrained model could forecast across domains without additional training (Garza, Challu & Mergenthaler-Canseco, 2023, arXiv:2310.03589), and Lag-Llama showed a decoder-only transformer using lags as covariates could generalise zero-shot and reach state of the art after fine-tuning on small fractions of unseen data (Rasul et al., 2023, arXiv:2310.08278). 2024 made it ordinary.

How Zero-Shot Forecasting Actually Works

Three design decisions do almost all the work, and they are the same three across every model in the family.

Scale has to go first

A model that sees electricity load in megawatts and river flow in cubic metres per second cannot share parameters between them unless scale is removed. Every pretrained forecaster normalises per instance, typically by dividing a context window by its own mean absolute value or by standardising it:

where \(L\) is the context length and \(\mu_c, \sigma_c\) are computed from that context alone, never from the full series and never from training statistics. The forecast is produced in normalised space and multiplied back afterwards.

This is not a preprocessing detail; it is a statement about what the model is allowed to learn. Absolute level is defined as uninformative. That is exactly right for transfer and exactly wrong when level carries meaning, which is why these models are poor at series with hard floors, saturation points or regulatory caps.

The series becomes tokens, one way or another

Chronos took the most literal route: scale the series, quantise the values into a fixed vocabulary of bins, and train an off-the-shelf T5 language model on the resulting token sequence with cross-entropy loss (Ansari et al., 2024, Chronos: Learning the Language of Time Series, TMLR, arXiv:2403.07815). No architectural innovation at all, which was the point: the paper's contribution was demonstrating that the language-modelling stack transfers if you frame the data correctly.

TimesFM took the route that has since become standard: non-overlapping patches. The input is chopped into contiguous windows of length \(p\), each projected to a model dimension, and a decoder-only stack predicts an output patch that need not be the same length as the input patch (Das, Kong, Sen & Zhou, 2024, ICML, arXiv:2310.10688). Longer output patches mean fewer autoregressive steps for a given horizon, which is a direct trade of flexibility against error compounding.

Quantisation and patching differ in what they lose. Binning discards resolution inside a bin, permanently, and the loss is worst in the tails where bins are widest. Patching preserves values but forces the model to treat a patch as an atomic unit, so a spike in the middle of a patch is smeared across the patch's representation. Neither is obviously better; both are why fine detail at the extremes is the first thing to degrade.

[IMAGE: A single noisy series drawn three times in a vertical stack: raw, after quantisation into visible horizontal bin bands, and after patching into shaded blocks of 32 points. Annotations mark one narrow spike, showing it surviving quantisation but flattening under patching, and one small oscillation, showing the reverse. Caption: "Two tokenisations, two different things thrown away."]

The objective decides what "forecast" means

Chronos predicts a categorical distribution over bins and samples from it, which gives a full predictive distribution at the cost of resolution. Most later models predict quantiles directly under pinball loss, which is sharper and cheaper but fixes the quantile grid at training time. Moirai used a mixture distribution with any-variate attention, trained as a masked encoder over the LOTSA archive of more than 27 billion observations across nine domains (Woo et al., 2024, arXiv:2402.02592).

The probabilistic output is the part practitioners under-use and the part that most justifies the models. A zero-shot point forecast is a commodity. A zero-shot calibrated interval on a series with 30 observations is something no classical method can produce, because there is nothing to estimate the variance from.

What in-context learning changed

The first generation was univariate by construction: one series in, one series out, no channel for anything else. That was a modelling choice and, as it turned out, the binding constraint.

Chronos-2 restructured around it. Its group attention mechanism shares information across a group of series, where a group can be related series, the variates of a multivariate series, or a target plus its covariates, and the model was trained on synthetic data that imposes diverse multivariate structures on univariate series so the mechanism has something to learn from (Ansari, Shchur et al., 2025, arXiv:2510.15821). The covariate is not a feature the model was fitted on; it is context supplied at inference, and the relationship between target and covariate is inferred in the forward pass.

That is a genuine capability change rather than a scaling result, and the numbers follow it. The same period produced TabPFN-TS, which achieved state-of-the-art covariate-informed accuracy with 11 million parameters by converting the series into a table of temporal features and applying a pretrained tabular model, no time-series pretraining involved (Hoo, Müller, Salinas & Hutter, 2025, arXiv:2501.02945). Two very different architectures, one shared lesson: access to covariates beat parameters.

[IMAGE: Two-panel diagram. Left panel, "univariate TSFM": one series enters a box, one forecast leaves, with a greyed-out promotion calendar sitting outside the box marked "not reachable". Right panel, "group attention": target series, two related series and a promotion calendar all enter a shared attention block, with arrows between them, and the forecast leaves with a visible promotional spike. Caption: "The covariate channel, not the parameter count, is what separates the generations."]

Seeing It in Motion

The serving path is where the operational argument for these models is won, and it looks nothing like a classical forecasting pipeline.

sequenceDiagram
    participant P as Planner
    participant S as Forecast service
    participant F as Feature store
    participant M as Pretrained model
    participant B as Fallback
    P->>S: forecast(series_id, horizon=28)
    S->>F: fetch context window and covariates
    F-->>S: 512 observations, promo calendar
    alt context length sufficient
        S->>M: scaled context plus covariate group
        M-->>S: quantiles q10 q50 q90
    else fewer than 30 observations
        S->>B: attribute-group prior
        B-->>S: cold-start quantiles
    end
    S->>S: rescale, clip to domain bounds
    S-->>P: distribution plus provenance flag
    Note over S,M: No fitting step anywhere in this path

The missing box is the interesting one. There is no training job, no per-series parameter store, no retraining cadence and no model-per-series registry. A classical pipeline serving 200,000 series has 200,000 parameter sets to fit, version, monitor and expire. This has one artefact and a feature join.

That is a real reduction in operational surface, and it is why teams adopt these models even when accuracy is a wash. It is also why the decision of when not to use them needs to be explicit, or the convenience will make it for you.

flowchart TB
    Q1{"History length?"}
    Q1 -->|"Under 30 points"| Z["Pretrained prior wins<br/>nothing else can fit"]
    Q1 -->|"30 to 300 points"| Q2{"Covariates that<br/>drive the target?"}
    Q1 -->|"Thousands of points"| Q3{"Cross-series<br/>structure?"}
    Q2 -->|"None"| Z2["Pretrained model<br/>competitive and cheap"]
    Q2 -->|"Promotions or prices"| C["Covariate-aware model<br/>group attention or global GBDT"]
    Q3 -->|"Many related series"| G["Global GBDT<br/>or fine-tuned TSFM"]
    Q3 -->|"One important series"| L["Fit it properly<br/>domain model plus combination"]

    classDef blue fill:#1e40af,stroke:#3b82f6,stroke-width:1px,color:#fff
    classDef purple fill:#6d28d9,stroke:#a78bfa,stroke-width:1px,color:#fff
    classDef emerald fill:#047857,stroke:#34d399,stroke-width:1px,color:#fff
    classDef amber fill:#b45309,stroke:#fbbf24,stroke-width:1px,color:#fff
    class Q1,Q2,Q3 purple
    class Z,Z2 emerald
    class C,G blue
    class L amber

Watch It Run

By the Numbers

Sources: Chronos (Ansari et al., 2024, arXiv:2403.07815); Chronos-Bolt figures are Amazon's own published claims, not independent measurement; TimesFM (Das et al., 2024, arXiv:2310.10688); Moirai (Woo et al., 2024, arXiv:2402.02592); Toto and BOOM (arXiv:2505.14766); TiRex (arXiv:2505.23719); TabPFN-TS (arXiv:2501.02945); Chronos-2 and its fev-bench skill scores (arXiv:2510.15821). Every accuracy figure in this table is self-reported by the model's authors on benchmarks they selected. Read the column as a claim, not a measurement.

The evaluation infrastructure deserves its own numbers. GIFT-Eval covers roughly two dozen datasets, 144,000 series and 177 million observations across seven domains, ten frequencies and horizons from short to long, and ships a deliberately non-leaking pretraining corpus of 88 datasets, 4.5 million series and 230 billion data points so that zero-shot claims can be made against a documented training set (Aksu et al., 2024, arXiv:2410.10393). fev-bench adds 100 realistic tasks spanning univariate, multivariate and covariate-informed forecasting (arXiv:2509.26468). Both exist because the previous generation of comparisons was not trustworthy.

A Concrete Example

Take a weekly retail series with a promotion in week 9. Twelve observations of units sold:

week:   1    2    3    4    5    6    7    8    9   10   11   12
units: 102   98  110   95  104   99  108  101  340  112   97  105

Step 1: instance scaling. Mean absolute value over the context is \(\bar{|y|} = 122.6\). Chronos-style mean scaling divides through:

0.83 0.80 0.90 0.77 0.85 0.81 0.88 0.82 2.77 0.91 0.79 0.86

Note what already happened. The promotion week is now 2.77 while every other week sits between 0.77 and 0.91. The scaling was computed including the spike, so the spike inflated the divisor and compressed the baseline into a narrow band.

Step 2: quantisation. Real implementations use a few thousand bins over a bounded range. Scale that down to 16 uniform bins over \([0, 3]\) for arithmetic you can do on paper, so each bin is 0.1875 wide. Values map to bin indices \(\lfloor \tilde{y}/0.1875 \rfloor\):

4  4  4  4  4  4  4  4  14  4  4  4

Eleven of twelve observations collapse into a single token. The model's entire view of this series is "constant, with one large excursion", and the 8% week-to-week variation that a demand planner cares about has been quantised away. Coarse binning is why quantised models are strong on shape and weak on small-amplitude structure.

Step 3: what the prior can and cannot express. Ask for week 13. The model has seen this pattern class many thousands of times in pretraining: flat baseline, isolated spike, return to baseline. It will predict the baseline, around token 4, with an upper quantile wide enough to acknowledge that spikes happen in this series. Decoded back through the scale, something like \(q_{50} \approx 103\), \(q_{90} \approx 180\).

Step 4: the number that matters. Suppose week 13 is another promotion and sells 355 units. Compute MASE against the in-sample seasonal-naive benchmark. For this series the mean absolute one-step naive error over weeks 2 to 12 is

The zero-shot forecast errs by \(|355 - 103| = 252\), giving a MASE of \(252/50.1 = 5.03\). A model that had the promotion calendar as a known-future covariate and had learned a multiplier of roughly 3.3 for promotional weeks would predict about 340, an error of 15 and a MASE of 0.30.

That gap, a factor of seventeen on this week, is not a modelling subtlety. It is the covariate. No amount of pretraining recovers information that was never in the input, and this is the single most common way zero-shot forecasting disappoints in production: it is evaluated on quiet weeks and deployed on the weeks that matter.

[IMAGE: Line chart of the twelve-week series with the week-13 actual marked as a dot at 355, three forecast markers overlaid: zero-shot median at 103 with a q10-q90 band reaching 180, covariate-aware forecast at 340 with a tight band, and seasonal naive at 105. Caption: "The interval is honest and still useless: the model widened its uncertainty instead of knowing the answer, because it could not see the promotion."]

Where It Breaks

Benchmark contamination, now measurable

The zero-shot claim rests entirely on the test series being absent from pretraining, and for most published models that is asserted rather than demonstrated, because pretraining corpora are large, heterogeneous and frequently undocumented.

This stopped being a rhetorical objection. TSFMAudit detects contamination through adaptation dynamics: a contaminated dataset adapts unusually efficiently under a fine-tuning probe, with faster loss reduction and smaller backbone movement than a genuinely unseen one. The authors evaluated it on 6 pretrained forecasters across 187 datasets against 10 baselines adapted from the LLM contamination literature (arXiv:2605.26161). A complementary analysis separates two leakage channels: direct overlap from reusing the same public datasets across training and evaluation, and indirect overlap where train and test series share a causal driver, the example given being COVID-19 distorting correlated financial series across geographies. Its conclusion is blunt: ignoring these turns benchmarks into measures of memorisation rather than generalisation (arXiv:2510.13654).

The right response is not to disbelieve the models but to evaluate on your own data with a test period that postdates the model's public release, treating any leaderboard position as a prior rather than a result. A study of electricity price forecasting does this explicitly, pairing a classic competition set with a newer market series chosen so public pretraining cutoffs predate the test year (arXiv:2607.02623).

Non-stationarity is not in the prior

Instance scaling normalises level and spread over the context window, which handles slow drift. It does not handle regime change, because a regime change means the relationship the model learned no longer holds, and nothing in the context tells it that. A series that shifts from one operating mode to another will be forecast as though the old mode continues, with intervals calibrated to the old mode's volatility, which is the worst combination: wrong and confident.

Calibration is corpus-relative

The predictive intervals are calibrated to the pretraining distribution, not to yours. If your series are more volatile than the corpus average at a given shape, coverage will be too low; if less, too high. Nothing about the zero-shot setting fixes this, and there is no validation set involved to catch it. Conformal post-processing with a small calibration window is cheap and almost always worth doing, and it is the single highest-value 20 lines of code in a TSFM deployment.

The LLM-flavoured versions were mostly not the LLM

A cautionary result sits next to this literature. Tan and colleagues ablated three popular LLM-based forecasting methods and found that removing the language model, or replacing it with a basic attention layer, did not degrade performance and in most cases improved it. Pretrained LLMs did no better than models trained from scratch, did not represent sequential dependencies, and did not help in few-shot settings; a simple patching-plus-attention baseline they call PAttn outperformed most of the LLM-based systems (Tan et al., NeurIPS 2024, arXiv:2406.16964).

That result is about repurposed language models, not purpose-built forecasters like Chronos or TimesFM, and conflating the two is a common error in both directions. It does establish the discipline this subfield needs: before believing a large pretrained component is doing the work, ablate it.

Cost is not obviously lower

A 200M-parameter forward pass per series per cycle is not free. For 200,000 series forecast daily that is 200,000 GPU inferences, where ETS would be microseconds of CPU each. The pretrained model wins on engineer-hours and loses on compute, and which dominates depends on catalogue size and refresh rate. Chronos-Bolt exists because of this: a reported 250x speedup over the original Chronos at equal size is an acknowledgement that the first generation was too slow to serve at scale.

The forecast is not the decision

None of these models know what the number is for. A forecast feeding replenishment needs the quantile matching the service level, coherence across the product hierarchy, and stability between runs, so planners are not chasing a number that moved 8% because the context window slid by a day. Zero-shot models give an unstable, incoherent, unconditioned distribution by default, and every one of those properties has to be added downstream.

[IMAGE: Two small multiples of the same 28-day forecast produced on consecutive days from a sliding context window, overlaid, with the difference shaded. Caption: "Run-to-run instability from a one-day context shift is invisible in accuracy metrics and immediately visible to planners."]

Alternative Designs

The Super-Linear line deserves emphasis because it targets the assumption everything else rests on. Its authors replace the deep backbone with simple frequency-specialised linear experts and a spectral gate, reporting strong benchmark performance with substantially better efficiency, robustness to sampling rate and interpretability (Nochumsohn et al., TMLR 2026, arXiv:2509.15105). If a mixture of linear models recovers most of the benefit, the useful part of pretraining may be the shape library rather than the representation depth.

[IMAGE: Scatter plot with parameter count on a log x-axis and reported benchmark rank on the y-axis, points labelled TabPFN-TS (11M), TiRex (35M), Chronos-2 (~100M), Toto (151M), TimesFM (200M), Chronos-Large (710M). Caption: "Across the 2025 cohort, parameter count and reported accuracy are close to uncorrelated. Architecture and data access explain the ranking; size does not."]

How It Is Used in Practice

The deployment pattern that has emerged is triage, not replacement.

The long tail goes zero-shot. Series with under a few hundred observations were never going to get a fitted model; before pretrained forecasters they got seasonal naive or a category average. Now they get a calibrated distribution for the cost of an inference call. This is where the honest gain is, and it is substantial precisely because the previous baseline was so weak.

The head keeps its pipeline. The few thousand series driving most of the revenue keep their global GBDT or supervised neural model with full covariates, hierarchy reconciliation and a tuned decision layer. The M5 result has not been overturned for this regime, and the worked example above shows why: a promotion calendar is worth more than a pretrained backbone.

The middle is where the measurement goes. Series with moderate history and some covariates are the contested band, and the only way to resolve it is a bake-off on your own data with a post-release test period. The crossing point between "prior wins" and "fit wins" as a function of history length is measurable for your domain, and it is usually not where anyone guessed.

Observability is its own case. Infrastructure metrics have extreme cardinality, heavy multivariate structure and very short usable history per metric. Toto was built for that setting with an observability-weighted pretraining corpus and released alongside BOOM, a benchmark of 350 million observations across 2,807 real-world series, precisely because general benchmarks did not represent the domain (arXiv:2505.14766). Expect more domain-specific pretraining for the same reason.

Fine-tuning is the under-used middle path. Lag-Llama reported state-of-the-art results after fine-tuning on small fractions of previously unseen data, and the pattern holds broadly: a few hundred steps on your corpus recovers most of the gap to a fully supervised model at a fraction of the engineering cost. Teams reach for zero-shot or for a full pipeline and skip the option between them.

[IMAGE: Three-column flow diagram of the triage pattern: "long tail, 180,000 series, zero-shot", "middle band, 15,000 series, fine-tuned or measured bake-off", "head, 3,000 series, full global pipeline with covariates and reconciliation", each column annotated with what it costs to run. Caption: "Adoption is a routing decision, not a migration."]

Insights Worth Remembering

1. A pretrained forecaster learned shapes, not your business. Everything it can do follows from having seen many instances of a small number of recurring patterns after scale was removed. It has no representation of a promotion, a price change or a competitor, and it never will unless you pass one in.

2. The covariate channel mattered more than four orders of magnitude of parameters. An 11M-parameter tabular model matched Chronos-Large at 65 times the size because it could see the covariates. When you are choosing between models, ask what each one is allowed to look at before you ask how big it is.

3. Instance scaling is a modelling assumption, not preprocessing. By normalising each context window, these models declare absolute level uninformative. That is what makes transfer work and what makes them weak on bounded, saturating or floor-constrained series.

4. Zero-shot means unaudited, not verified. The claim requires your data to be absent from a pretraining corpus you cannot inspect. Contamination auditing now exists because assertion was not good enough, and the practical defence is a test period that postdates the model's release.

5. The interval is the product. A point forecast from a pretrained model is replaceable by a dozen cheaper methods. A calibrated predictive distribution on a series with 30 observations is not, and it is the capability most deployments fail to use.

6. Calibration is inherited from the corpus and should be corrected locally. Coverage on your series is an empirical question with an easy answer: measure it, then conformalise against a small recent window. Skipping this is how a technically impressive model produces intervals nobody trusts.

7. Operational simplicity is a real accuracy-independent benefit. No fitting, no per-series artefacts, no retraining schedule and no cold-start branch is worth adopting for even at parity. Just be explicit that you bought simplicity, not accuracy, so nobody later reports it as the latter.

8. Every headline number in this field is currently self-reported. The models are evaluated by their authors on benchmarks their authors selected, sometimes benchmarks their authors built. That is not misconduct, it is the normal state of a young subfield, and it means independent replication is the scarce good.

Open Questions

Does scaling pretraining still buy accuracy? Measured: the 2025 cohort shows little correlation between parameter count and reported rank, with a 35M model competing against a 710M one. Unknown: whether that is a ceiling on what univariate shape priors can capture, or simply that no comparison has held data curation and architecture constant.

How much of the reported zero-shot advantage survives strict contamination control? Measured: contamination is detectable and both leakage channels have been characterised. Not yet measured: the size of the correction. Nobody has re-run a major leaderboard under the strict global post-training test period the leakage analysis calls for.

Can in-context covariate learning match a fitted covariate model? Measured: Chronos-2 reports the best public results on covariate-informed fev-bench tasks. Open: whether inferring a target-covariate relationship in a forward pass matches estimating it from thousands of examples when the relationship is stable. Expect fitting to win with enough data; the empirical question is where the crossover sits.

Is the useful content of pretraining a shape library or a learned representation? The Super-Linear result, where a gated mixture of frequency-specialised linear experts recovers strong performance, is suggestive rather than decisive. If the shape-library reading is right, most of the benefit is available at a fraction of the inference cost.

What does a pretrained model do to forecast stability? Largely unstudied. Planners depend on forecasts not moving arbitrarily between runs, and a model whose output depends on a sliding context window through a non-linear backbone carries no stability guarantee. Run-to-run variation under a one-day context shift is an easy experiment that almost nobody publishes.

Sources and Further Reading

1. Ansari, A. F., Stella, L., Turkmen, C., et al. (2024). "Chronos: Learning the Language of Time Series." Transactions on Machine Learning Research. arXiv:2403.07815
2. Ansari, A. F., Shchur, O., Küken, J., Auer, A., et al. (2025). "Chronos-2: From Univariate to Universal Forecasting." arXiv:2510.15821
3. Das, A., Kong, W., Sen, R., & Zhou, Y. (2024). "A decoder-only foundation model for time-series forecasting." Proceedings of the 41^st International Conference on Machine Learning. arXiv:2310.10688
4. Woo, G., Liu, C., Kumar, A., et al. (2024). "Unified Training of Universal Time Series Forecasting Transformers." ICML 2024. arXiv:2402.02592
5. Auer, A., et al. (2025). "TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning." NeurIPS 2025. arXiv:2505.23719
6. Cohen, B., et al. (2025). "This Time is Different: An Observability Perspective on Time Series Foundation Models." arXiv:2505.14766
7. Hoo, S. B., Müller, S., Salinas, D., & Hutter, F. (2025). "From Tables to Time: Extending TabPFN-v2 to Time Series Forecasting." arXiv:2501.02945
8. Rasul, K., Ashok, A., Williams, A. R., et al. (2023). "Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting." arXiv:2310.08278
9. Garza, A., Challu, C., & Mergenthaler-Canseco, M. (2023). "TimeGPT-1." arXiv:2310.03589
10. Aksu, T., Woo, G., Liu, J., et al. (2024). "GIFT-Eval: A Benchmark for General Time Series Forecasting Model Evaluation." arXiv:2410.10393
11. Shchur, O., et al. (2025). "fev-bench: A Realistic Benchmark for Time Series Forecasting." arXiv:2509.26468
12. "TSFMAudit: Data Contamination Auditing in Forecasting Time Series Foundation Models." (2026). arXiv:2605.26161
13. "Rethinking Evaluation in the Era of Time Series Foundation Models: (Un)known Information Leakage Challenges." (2025). arXiv:2510.13654
14. Tan, M., Merrill, M. A., Gupta, V., Althoff, T., & Hartvigsen, T. (2024). "Are Language Models Actually Useful for Time Series Forecasting?" NeurIPS 2024. arXiv:2406.16964
15. Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2022). "M5 accuracy competition: Results, findings, and conclusions." International Journal of Forecasting, 38(4), 1346-1364. doi:10.1016/j.ijforecast.2021.11.013
16. Elsayed, S., Thyssens, D., Rashed, A., & Schmidt-Thieme, L. (2021). "Do We Really Need Deep Learning Models for Time Series Forecasting?" arXiv:2101.02118
17. Nochumsohn, L., Marshanski, R., Zisling, H., & Azencot, O. (2026). "Super-Linear: A Lightweight Pretrained Mixture of Linear Experts for Time Series Forecasting." TMLR. arXiv:2509.15105
18. "Evaluating Time Series Foundation Models for Electricity Price Forecasting: Contamination Risk, Distributional Shifts, and Covariate Dependence." (2026). ICML 2026 Foundation Models for Structured Data Workshop. arXiv:2607.02623

Free to read, no ads, no sign-up. If it was useful you can buy me a coffee.