Zero-Shot Time-Series Forecasting

• Zero-shot time-series forecasting is a technique where pre-trained models predict future values on unseen series without fine-tuning, ensuring adaptability across domains.
• It leverages diverse architectures—including transformer-based TSFMs, synthetic-prior PFNs, and frozen LLMs—with patch-based and in-context modeling for handling heterogeneous data.
• Empirical studies show competitive performance on various benchmarks, supporting unified interfaces and retrieval-augmented strategies to enhance forecasting accuracy.

Zero-shot time-series forecasting denotes the production of forecasts for a new time series without any task-specific training or re-training on that series, and in some formulations without any adaptation to its domain. In the canonical formulation, a pre-trained forecaster with fixed parameters $\theta^\star$ is applied directly to history $x_{1:T}$ and optional covariates to produce $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$, shifting forecasting from dataset-specific estimation toward reuse of general-purpose models. The resulting literature spans time-series foundation models trained on large real and synthetic corpora, prior-data fitted networks trained purely on synthetic priors, latent in-context predictors, state-space foundation models, frozen LLM forecasters based on numerical tokenization, retrieval-augmented systems, and model-zoo routers (Dai et al., 25 Jun 2026, Xiao et al., 6 Mar 2025, Dooley et al., 2023).

1. Formal setting and relation to classical forecasting

In the standard supervised setting, a model $f_\theta$ is trained on input–target windows such as $(x_{t-L+1:t}, x_{t+1:t+H})$ and optimized on the downstream dataset. Zero-shot forecasting removes that downstream optimization stage. A pre-trained model is learned once on a large corpus of heterogeneous series and then reused directly on previously unseen series and datasets, with no gradient updates at deployment (Dai et al., 25 Jun 2026).

A common formalization writes the history as $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$ and the task as $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$. This formulation is frequently univariate, but the literature uses several extensions. Some models treat multivariate data in a channel-independent way, forecasting each variable separately with the same model; others use sets of related series as context, so that zero-shot adaptation occurs through in-context conditioning rather than parameter updates (Xiao et al., 6 Mar 2025, Verdenius et al., 2024).

A stricter variant appears in frozen-LLM work, where zero-shot means not only no task-specific fine-tuning, but also no training on any time-series data at all for the deployed model. In that setting, forecasting is performed entirely through prompting and tokenization of numerical sequences, and any robustness improvements must arise from input-side manipulations rather than parameter adaptation (Yin et al., 23 Dec 2025).

2. Major methodological families

The field is heterogeneous in both pre-training source and inference mechanism. A useful organizing distinction is between large-corpus TSFMs, synthetic-prior PFN-style models, frozen LLM forecasters, and systems that augment or route among pre-trained forecasters.

Family	Representative systems	Characteristic mechanism
Large-corpus TSFMs	TimesFM, Chronos, Moirai, TimeFound	Pre-train once on large real and synthetic corpora; reuse zero-shot
Synthetic-prior PFNs	ForecastPFN	Approximate Bayesian inference under a synthetic prior
Latent in-context models	LaT-PFN	JEPA-style latent space plus PFN-style in-context inference
State-space zero-shot models	Mamba4Cast	Mamba2 backbone with PFN-style synthetic training
Frozen LLM forecasters	LLMTime, MultiCast, NLTS	Numerical tokenization and next-token prediction
Retrieval and routing systems	TimeRAF, QuiZSF, SeqFusion, ZooCast	External retrieval or model-zoo selection on top of PTMs

Large-corpus TSFMs include decoder-only, encoder–decoder, and masked-encoder architectures trained across heterogeneous domains and frequencies. TimesFM is a decoder-only, patch-based transformer trained on a large time-series corpus and used zero-shot without gradient updates; TimeFound is an encoder–decoder transformer with multi-resolution patching and two released scales, 200M and 710M parameters, trained on a corpus of real-world and synthetic datasets; Moirai and Chronos are foundation-model variants emphasizing, respectively, universal patch-based forecasting and tokenized “language of time series” modeling (Das et al., 2023, Xiao et al., 6 Mar 2025, Jetwiriyanon et al., 30 May 2025).

Synthetic-prior PFNs replace broad real-data pre-training with explicit synthetic generative priors. ForecastPFN is trained purely on synthetic time series drawn from a prior with multi-scale Fourier seasonality, linear and exponential trends, and multiplicative Weibull noise, and learns to approximate the posterior predictive mean in a single forward pass. LaT-PFN extends the PFN line by moving inference into a JEPA-style latent space and using related series as context, while Mamba4Cast uses a Mamba2 state-space backbone trained solely on synthetic data generated from ForecastPFN-style components and Gaussian-process priors (Dooley et al., 2023, Verdenius et al., 2024, Bhethanabhotla et al., 2024).

Frozen-LLM forecasters treat time-series forecasting as text continuation. The defining operation is tokenization: numerical values are converted into textual tokens, often digits separated by commas, and the LLM is asked to continue the sequence. MultiCast extends this paradigm to multivariate data through token multiplexing, while NLTS shows that in a fully off-the-shelf setting, inference-time noise injection before tokenization can improve robustness (Gruver et al., 2023, Chatzigeorgakidis et al., 2024, Yin et al., 23 Dec 2025).

3. Architectural mechanisms that enable zero-shot transfer

Patch-based modeling is one of the dominant inductive biases. TimesFM splits a univariate history into non-overlapping patches of length $p$, treats those patches as tokens, applies a decoder-only transformer with causal attention, and predicts longer output patches of length $h$, with $h$ typically larger than $x_{1:T}$0. This reduces effective sequence length, improves long-horizon efficiency, and supports blockwise autoregression at inference (Das et al., 2023).

TimeFound generalizes patching to multiple resolutions. It uses patch sizes $x_{1:T}$1, projects each patch and its mask through a resolution-specific MLP, aligns coarse and fine token streams by replication to the highest-resolution length, and fuses them by summation. The encoder uses bidirectional self-attention over historical patches, the decoder uses causal self-attention plus cross-attention, and forecasting proceeds patch-by-patch with output patch size $x_{1:T}$2. This architecture is explicitly motivated by zero-shot generalization across domains with different intrinsic time scales (Xiao et al., 6 Mar 2025).

Several works emphasize latent or in-context structure rather than only sequence scaling. LaT-PFN maps series onto a normalized abstract time interval, learns a prediction-optimized latent representation with a JEPA-style target encoder, and performs PFN-style in-context forecasting in latent space using sets of related series as context. This permits arbitrary time granularity and forecast horizon within a single trained model, and the paper reports the emergence of patch-like embeddings even without explicit patch training (Verdenius et al., 2024).

State-space alternatives replace quadratic self-attention with linear-time recurrence. Mamba4Cast uses a Mamba2 backbone with causal convolutions and predicts the entire horizon in one pass rather than autoregressively. Its recurrence is of the form $x_{1:T}$3, $x_{1:T}$4, and its training prior mixes Gaussian-process and ForecastPFN-style synthetic generators. The reported effect is stronger scaling with prediction length than transformer-based foundation models (Bhethanabhotla et al., 2024).

LLM-based approaches rely on tokenization rather than architectural specialization. LLMTime encodes values as strings of numerical digits and frames forecasting as next-token prediction. MultiCast adds digit-interleaving, value-interleaving, and value-concatenation to multiplex multivariate series into a one-dimensional token stream, optionally preceded by SAX quantization to reduce token count. NLTS retains the frozen-LLM setting but perturbs raw time series with zero-mean noise before tokenization, arguing that this encourages extrapolation based on stable temporal structure rather than superficial numerical artifacts (Gruver et al., 2023, Chatzigeorgakidis et al., 2024, Yin et al., 23 Dec 2025).

4. Evaluation protocols and empirical landscape

Evaluation is fragmented across benchmarks, metrics, and operational definitions of zero-shot. A systems-oriented validation in Darts used fev-bench-mini, a subset of fev-bench, and reported skill scores relative to a seasonal naive baseline. Darts Chronos-2 achieved SQL skill $x_{1:T}$5 and MASE skill $x_{1:T}$6, compared with $x_{1:T}$7 and $x_{1:T}$8 in the original Chronos-2 implementation; Darts TiRex achieved SQL skill $x_{1:T}$9 and MASE skill $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$0 versus $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$1 and $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$2 originally; Darts TimesFM 2.5 achieved SQL skill $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$3 and MASE skill $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$4 versus $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$5 and $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$6 originally. The reported differences are at most about 1.3 percentage points, indicating that a unified interface need not materially degrade zero-shot accuracy (Dai et al., 25 Jun 2026).

Modeling papers report stronger task-level claims. On 24 unseen datasets, TimeFound-Large achieved the best average MASE, $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$7, compared with $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$8 for TimeFound-Base, $$\hat{x}_{T+1:T+H} = f_{\theta^\star}(x_{1:T}, \text{covariates})$$9 for Chronos-Base, $f_\theta$0 for Chronos-Large, and $f_\theta$1 for TimesFM; its sMAPE was $f_\theta$2, tied with TimeFound-Base and slightly above TimesFM’s $f_\theta$3. On rolling long-horizon evaluation over ETT datasets, TimeFound-Large obtained the best or tied-best averages in several cases, including ETTh1 average MAE $f_\theta$4 and sMAPE $f_\theta$5, ETTm1 average MAE $f_\theta$6 and sMAPE $f_\theta$7, and ETTm2 average MAE $f_\theta$8 and sMAPE $f_\theta$9 (Xiao et al., 6 Mar 2025).

Synthetic-prior and latent models target data-scarce settings. ForecastPFN reports about $(x_{t-L+1:t}, x_{t+1:t+H})$0 seconds to obtain predictions on a new dataset and dominates low-data and low-time-budget settings in its experiments, even when competing methods are allowed to train on in-distribution samples. LaT-PFN reports lower MSE than ARIMA, FBProphet, and ForecastPFN on several benchmarks, including ECL MSE $(x_{t-L+1:t}, x_{t+1:t+H})$1 versus $(x_{t-L+1:t}, x_{t+1:t+H})$2, $(x_{t-L+1:t}, x_{t+1:t+H})$3, and $(x_{t-L+1:t}, x_{t+1:t+H})$4, and Illness MSE $(x_{t-L+1:t}, x_{t+1:t+H})$5 versus $(x_{t-L+1:t}, x_{t+1:t+H})$6, $(x_{t-L+1:t}, x_{t+1:t+H})$7, and $(x_{t-L+1:t}, x_{t+1:t+H})$8 (Dooley et al., 2023, Verdenius et al., 2024).

Zero-shot performance is not confined to transformer TSFMs. Mamba4Cast reports a geometric mean MASE of $(x_{t-L+1:t}, x_{t+1:t+H})$9 with a training prior mix of $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$0 Gaussian-process and $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$1 ForecastPFN-based series, outperforming the corresponding $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$2 GP and $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$3 ForecastPFN priors, and shows that multi-point forecasting is substantially better than autoregressive use, with geometric mean MASE $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$4 versus $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$5. Frequency-targeted synthetic training can also alter the zero-shot landscape: Freq-Synth reduced average MSE relative to real-data zero-shot training for TTM from $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$6 to $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$7, for Timer from $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$8 to $\mathbf{x}_{1:C} = \{x_1, x_2, \ldots, x_C\}$9, for UniTime from $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$0 to $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$1, for MOMENT from $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$2 to $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$3, for GPT4TS from $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$4 to $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$5, and for PatchTST from $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$6 to $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$7 across eight datasets (Bhethanabhotla et al., 2024, Nochumsohn et al., 2024).

5. Retrieval, routing, and unified tooling

A recurring systems observation is that zero-shot forecasting has moved beyond monolithic standalone models. The Darts integration paper argues that foundation models are often released as isolated packages with fragmented interfaces and limited interoperability. Its FoundationModel abstraction wraps Chronos-2, TimesFM 2.5, TiRex, and PatchTST-FM under the same fit, predict, historical_forecast, and backtest interface used by other Darts models, while preserving access to covariates, backtesting, residual analysis, uncertainty estimation, mixed precision, and SHAP-based explainability (Dai et al., 25 Jun 2026).

Retrieval-augmented forecasting turns zero-shot prediction into a hybrid parametric–nonparametric problem. TimeRAF adds a learnable retriever and a Channel Prompting module around a frozen TTM-Base backbone, using a large time-series knowledge base built from LOTSA and UTSD. On six zero-shot datasets with horizon 96, TimeRAF improved over plain TTM$f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$8 on ETTh1, ETTh2, ETTm2, Weather, and Electricity, and the authors report that TimeRAF outperformed both plain TTM zero-shot and TTM fine-tuned with 5% labeled data on all datasets in a specific comparison (Zhang et al., 2024). QuiZSF pushes the same idea further with a hierarchical ChronoRAG Base, a Multi-grained Series Interaction Learner, and a dual-branch Model Cooperation Coherer, reporting Top-1 ranking in $f:\mathbf{x}_{1:C}\rightarrow \mathbf{x}_{C+1:C+H}$9 of non-LLM zero-shot settings and $p$0 of LLM-based transfer settings (Ma et al., 9 Aug 2025).

Routing across pre-trained models addresses another empirical regularity: no single TSFM wins everywhere. ZooCast formalizes this by embedding both tasks and models into a shared representation space and ranking TSFMs via similarity to model-specific “advantage subsets”; on GIFT-Eval, its Top-5 ensemble reached sMAPE $p$1 and the best average rank among reported methods. SeqFusion takes a related model-zoo view, but emphasizes privacy-preserving reuse of multiple smaller PTMs and variate-wise selection in a learned representation space, achieving competitive performance against both classical zero-shot baselines and large foundation models (Shi et al., 4 Sep 2025, Huang et al., 4 Mar 2025).

6. Limitations, misconceptions, and open problems

A central misconception is that zero-shot implies universal superiority. Multiple sources reject that claim. The Darts paper notes weaknesses under strong domain shift, unusual sampling rates, or highly irregular dynamics; the macroeconomic study finds that zero-shot TSFMs can match or exceed classical models during stable economic conditions, but are vulnerable to degradation in performances during periods of rapid shocks; and the model-zoo literature explicitly states that no single TSFM excels universally (Dai et al., 25 Jun 2026, Jetwiriyanon et al., 30 May 2025, Shi et al., 4 Sep 2025).

Frequency mismatch is a second major limitation. Freq-Synth identifies “frequency confusion,” where train sets containing target frequencies plus unrelated frequencies degrade performance, and “poor frequency generalization,” where models perform poorly on frequencies unavailable during training. The paper further shows that train–test periodogram similarity is a better predictor of zero-shot transfer than sector similarity or even belonging to the same underlying dataset with a different sampling rate. This suggests that part of zero-shot failure is spectral rather than merely statistical or semantic (Nochumsohn et al., 2024).

Frozen-LLM forecasting adds its own controversies. LLMTIME-style methods demonstrate that LLMs can function as zero-shot forecasters by converting time series into strings of digits, but the same line of work also shows brittleness to tokenizer design. NLTS argues that performance in the strict off-the-shelf setting is acutely sensitive to the textual representation of the input data, and proposes inference-time noise injection as a remedy. It further introduces contamination-resistant benchmarks to address the concern that reported gains might reflect memorization rather than genuine zero-shot extrapolation (Gruver et al., 2023, Yin et al., 23 Dec 2025).

Finally, benchmarking practice remains unsettled. Some evaluations use last-window protocols, others use rolling windows; some report point metrics only, others skill scores or probabilistic losses; leakage remains an explicit issue in at least one Darts validation case, where TimesFM 2.5 has one dataset overlapping with its training corpus. A plausible implication is that future work will depend as much on evaluation design, retrieval infrastructure, and interoperability as on new backbone architectures. The present literature already points in that direction through unified APIs, retrieval-augmented zero-shot systems, and model-zoo routers (Dai et al., 25 Jun 2026, Zhang et al., 2024, Shi et al., 4 Sep 2025).