energy demand planners

Abstract: We introduce Timestral, a family of four time series foundation models for probabilistic forecasting, with 5M, 28M, 123M, and 209M parameters. Timestral sets a new state of the art on GIFT-Eval, TIME, and fev-bench, where Timestral-209M and Timestral-123M take the top two places on every metric. We achieve this with three ingredients: Decoupled Horizon Forecasting (DHF), which separates prediction tokens from the causally encoded context, so that longer horizons are trained without masking context and each observed value is both a forecast target and context for later forecasts; a covariate framework that natively supports known-future covariates within a causal architecture; and a two-stage pipeline that pretrains exclusively on a diverse, large-scale synthetic corpus before post-training on a mix of real and synthetic data with extended context. This report describes the model design and its benchmark results. Weights for all four models are available on Hugging Face and inference code on GitHub.

Abstract: A central challenge in multivariate forecasting is deciding what to share across channels and where to specialize. Mixture-of-experts models offer flexible sharing, yet it remains unclear how much of their forecasting gains comes from added capacity or expert allocation. Through controlled comparisons across eleven datasets and three backbones, we show that informative channel assignments improve forecasting beyond matched shared capacity and random allocation. On frozen transformer backbones, persistent channel-specific mixtures outperform input-dependent routing on average. To examine when and how much specialization helps, we introduce GalaxyTS, a controlled synthetic dataset with exact shared and channel-specific forecasting references. It reveals how persistent channel mixtures exploit predictive differences concealed by short input windows and measures gains over matched shared corrections. These insights motivate Persistent Closed-Form Routing (PCR), a plug-and-play method that alternates exact conditional estimation of channel-specific mixture weights with gradient-based training of low-rank residual experts around a frozen pretrained forecaster. Averaged over four forecasting horizons, PCR-K4 achieves dataset-balanced mean squared error reductions of 3.86-14.25% relative to the three frozen backbones. In matched comparisons, PCR outperforms competing specialization methods on average while requiring substantially fewer trainable parameters.

Abstract: A universal forecaster is trained once and applied everywhere, so it must serve tasks whose schemas, forecast horizons, and temporal resolutions all differ. The number of targets and covariates changes from dataset to dataset, horizons vary by orders of magnitude, and sampling rates range from seconds to years. Existing time-series foundation models address these only in part, since they isolate each series or visit the two grid relations in separate blocks, and they fix the horizon and resolution before training begins. We introduce Morpheus-2.0, a compact encoder-only foundation model that represents targets and covariates on a single variable-time grid. Its dual-axis attention runs both relations side by side in every layer, one across variables at a timestep and one across time within a variable; a learned gate weights the two per layer, and an axis-aware rotary encoding preserves both grid coordinates. The forecast length is sampled during training, so one set of weights spans short to long horizons at no additional inference cost. Morpheus-2.0 Multiscale extends the model to several temporal resolutions at once, weighting them according to the series being forecast. Across GIFT-Eval, which spans several domains and frequencies, the two models give complementary operating points: Morpheus-2.0 attains 0.685 relative MASE with 81M parameters, while the larger Morpheus-2.0 Multiscale attains 0.646 relative MASE and 0.455 relative CRPS, the lowest of any published system on both metrics.

Abstract: Time series forecasting models are increasingly deployed in continuously evolving environments. After a forecast is issued, future observations gradually arrive and reveal how the model has failed. Existing methods mainly treat such observations as supervision for parameter updates. However, it remains unclear whether verified forecasting errors can themselves provide causal feedback for correcting future predictions. To address this, we introduce Error Feedback Calibration (EFC), a fully test-time framework for deterministic post-hoc correction of time series forecasting. EFC constructs a Causal Error Diagonal (CED) from revealed errors of overlapping historical forecasts, providing a fresh view of the frozen forecaster's recent failure behavior. Then Cumulative Error Transport (CET) maps this error state to future residuals using cumulative estimation, while temporal out-of-sample validation controls the correction strength. Temporal Residual Learning (TRL) further predicts only the residual structure left after CET from recent CED trajectories, rather than relearning the entire forecasting error. Extensive experiments across forecasting backbones and datasets show that EFC broadly improves forecasting performance while substantially controlling harmful over correction.

Abstract: Series decomposition has emerged as a widely acknowledged paradigm in deep time series forecasting models. However, existing approaches predominantly employ a homogeneous modeling strategy for all subsequences, thereby overlooking the distinct inductive biases inherent in different components. We identify that the trend component exhibits dominant spatial coupling across channels but carries significant temporal redundancy, whereas the seasonal component is characterized by local temporal evolution but remains susceptible to attention distraction. To address this, we propose a novel disentangled architecture that tailors specific modeling strategies to align with the intrinsic properties of each component. For the trend branch, we design a Latent Graph Block, employing latent graph modeling to capture global topological dependencies and system-wide co-movements. Conversely, for the seasonal branch, we introduce a Gaussian Multi-scale Attention mechanism to mitigate attention distraction. By injecting learnable Gaussian priors, we impose structural constraints that compel the model to focus on multi-granular local contexts, effectively filtering out global noise and accurately capturing local evolutionary phases. Extensive experiments on multiple real-world benchmarks demonstrate the effectiveness of our proposed model.

Abstract: Although multivariate time series forecasting has broad application prospects, effectively incorporating exogenous variables remains challenging. Prevailing discrete-time architectures often impose rigid temporal alignment across heterogeneous variables, which may limit their ability to capture continuously evolving external effects. To address this limitation, we introduce CTIA-ODE, a continuous-time forecasting framework centered on Continuous-Time Inter-Variable Attention (CTIA). Specifically, CTIA is embedded within an ordinary differential equation (ODE) solver, enabling the continuously evolving endogenous trajectory to dynamically query a static exogenous context along the integration path without requiring explicit temporal alignment. To improve the stability of the continuous latent dynamics, we further introduce a dual-stabilization strategy: architecturally, a Linear Residual Augmentation (LRA) module provides a macroscopic trend anchor, while an Outlier-Robust Hybrid Loss (ORHL) mitigates the influence of heavy-tailed anomalies during optimization. Extensive experiments across eight real-world datasets demonstrate that CTIA-ODE achieves state-of-the-art forecasting performance across diverse datasets and prediction horizons, while maintaining a favorable accuracy-efficiency trade-off with a compact memory footprint and low inference latency, particularly under long-horizon forecasting settings. Anonymous code is available at https://anonymous.4open.science/r/CTIA-ODE-15A6/.

Abstract: Time-series foundation models provide strong zero-shot forecast, but deployment for real- world applications still requires task-specific designs for model inputs and outputs. Direct inference can leave domain knowledge and re- curring forecast errors unaddressed, while tai- lored pipelines require substantial human ex- pertise and effort. We introduce TIMERSI, a self-improving agentic deployment system around frozen forecasting models. A cod- ing agent translates task descriptions into ex- ecutable pipeline changes. It tests each re- vision on historical forecasting windows and uses observed errors to guide subsequent re- visions. During deployment, an adaptive se- lector chooses among the resulting pipelines using completed forecasts under similar con- ditions. Across 198 tasks on TIME and FEV- bench, TIMERSI outperforms all submissions on six point and probabilistic forecasting met- rics. Controlled comparisons support the value of feedback-guided revision over non-iterative pipeline search. Further experiments verify the generalization with different coding agents and forecasting models.

Abstract: Accurate uncertainty quantification is critical for many time series forecasting applications, and recent studies have increasingly adopted generative models to capture predictive uncertainty. Existing approaches often combine deterministic forecasting with generative modeling to improve predictive performance. However, their joint training is typically unstable because the deterministic model is embedded within the generative process, resulting in deep computational graphs and changing the probability transport path. In this work, we propose DV-Flow, a unified flow-matching formulation that incorporates the deterministic predictor as a parallel velocity component rather than as the endpoint of the transport path. This design enables stable end-to-end optimization while subsuming several existing formulations as special cases, allowing direct comparisons among them. Extensive experiments on six real-world datasets demonstrate that DV-Flow consistently improves probabilistic forecasting performance over strong baselines. Our code is available at https://github.com/tufts-ml/dv-flow-time-series.

Abstract: Long-term time series forecasting requires temporal dependency modeling that remains stable and generalizable under temporal distribution shifts. However, real-world time series are often noisy and non-stationary, making deep learning models prone to fitting incidental temporal interactions in the training data. A key question is whether there exist temporal relationship structures that recur across different temporal positions and variables. We analyze temporal relationship matrices on commonly used time series datasets and find that samples from different temporal positions and different variables exhibit shared dominant temporal relationship structures. This indicates that temporal relationship structures contain patterns that recur stably across samples and variables. To learn such shared structures, we propose \textbf{T}emporal \textbf{Struct}ure Network (\textbf{TStruct}), a simple yet effective network for directly learning shared and generalizable temporal dependencies. Specifically, TStruct directly parameterizes a set of shared temporal dependency matrices and generates normalized combination weights using dynamic sample information and static variable priors. These weights represent a soft allocation of each sample-variable pair over shared temporal dependency structures, enabling the model to generate adaptive temporal dependency matrices under shared structural constraints, rather than fitting incidental interactions in a fully unconstrained manner. Notably, this simple structure-aware design consistently outperforms several strong baselines across all datasets, achieving superior accuracy while maintaining high computational efficiency.

Abstract: Multivariate long-horizon forecasting is critical to electricity load scheduling and traffic flow management, and to financial risk control. Existing deterministic backbones output a single trajectory, masking heterogeneous prediction difficulty across horizons and channels and providing no localized reliability signal. We present CARE (Corrective branch with Aligned context and Relative-error Estimation), a lightweight plug-in that enhances any deterministic forecaster without architectural redesign. Operating in parallel with the base model, CARE resamples historical context to match the forecast horizon, learns residual correction patterns from this aligned history, and applies scale-aware bounded updates modulated by per-coordinate sigmoid risk gates. A multi-objective loss jointly optimizes forecast accuracy, residual tracking, risk alignment, and base-model anchoring. Across eight benchmarks with three representative backbones, CARE improves accuracy with marginal parameter and latency overhead. Its risk gates reliably identify high-error regions: on Weather, the highest-gate tertile exhibits nearly four times the error of the lowest-gate tertile, offering planners an interpretable per-step trust signal. Code is available at https://github.com/CG-BNYC/CARE.

Abstract: Differentially private time-series generators commonly produce fixed-length synthetic windows, whereas downstream forecasting models often require long continuous training sequences. How these windows are assembled after generation can therefore alter the effective synthetic data presented to a forecaster, even when the trained generator remains unchanged. We study this post-generation sequence assembly process by systematically varying overlap rates and window-weighting schemes and evaluating the resulting sequences in terms of boundary continuity, statistical and temporal fidelity, and Train-on-Synthetic-Test-on-Real (TSTR) forecasting utility. Across four types of public datasets (ETTh1, ETTm1, Weather, and Appliances) and five forecasting models, the results reveal a clear forecaster-dependent assembly principle: downstream TSTR utility is jointly shaped by the forecaster, overlap rate, and window-weighting scheme, leading to distinct assembly preferences across forecasting models. Increased overlap generally improves boundary continuity, but improvements in continuity or individual fidelity diagnostics do not consistently reduce forecasting error, indicating that these diagnostics alone are insufficient for selecting assembly configurations. Complete five-forecaster assembly grids, together with matched Train-on-Real-Test-on-Real (TRTR) references, further characterize these regularities and quantify assembly-dependent utility relative to real-data training. We then validate the identified principles through additional analyses of robustness and generator variability.

Abstract: Recent work has shown that probabilistic flow matching for time series forecasting benefits from a data-matched prior. The resulting prior introduces local correlations, which a sequential architecture usually absorbs: a recurrent neural network (RNN), a structured state-space model (S4), or a Transformer. However, such a backbone costs GPU memory and time per epoch. A cheaper alternative is MLP-based latent-space flow matching: embed the time series via an invertible map to a single latent vector and learn the flow there, so a tabular MLP can treat the series as a set of features. The relationship between the prior and the choice of linear latent map is understudied in conditional flow matching (CFM) forecasting, yet we found it strongly affects performance. Fixed transforms such as Fourier or discrete cosine (DCT) are only well-conditioned for Ornstein--Uhlenbeck priors, while a principal-component (PCA) map fit to the data is a strong but training-set-dependent reference sensitive to train--test shift. Instead, we propose to use the Mercer eigenbasis of the prior kernel: it diagonalises the centred covariance exactly, decouples from training data, and adapts to non-stationary and periodic priors. On five GluonTS benchmarks (ETTh1, ETTh2, Weather, Electricity, Traffic) under a shared protocol with TSFlow, the resulting MLP matches or beats it on CRPS at about $4.7\times$ less training memory and $3.5\times$--$4.4\times$ less time per epoch.

Abstract: Time-series foundation models (TSFMs) enable zero-shot forecasting through large-scale cross-domain pretraining, while retrieval augmentation further improves their performance by leveraging historical information. However, existing methods typically correct TSFM forecasts using the ground-truth futures of similar historical windows, which contain both predictive components already captured by the foundation model and sample-specific random fluctuation that is difficult to transfer. In contrast, recurring systematic model bias within prediction errors more directly characterizes the failure modes of a frozen TSFM and therefore provides more valuable correction signals. Effectively exploiting such model bias, however, poses two challenges: prediction errors at different numerical levels are difficult to compare due to scale differences, and the recurring bias must be extracted from prediction errors contaminated by random fluctuation. To address these challenges, we propose GRAM, a general retrieval-augmented framework for frozen TSFMs. GRAM first introduces an Amplitude Memory Module (AMM) that scales prediction errors by amplitude and aggregates them into retrievable prototypes. It then employs a Prototype Graph Module (PGM) to model relations among prototypes to aggregate consistent bias information while suppressing random fluctuation. During online forecasting, GRAM retrieves and expands prototypes relevant to the current query and generates per-horizon corrections to refine the original TSFM forecast. Experiments across multiple datasets and foundation models demonstrate consistent forecasting improvements.

Abstract: Long-term forecasting models commonly process all patches in a look-back window using the same fixed stack. Older contextual patches and recent evidence therefore receive the same computational depth. Yet the information closest to the forecast and the more distant context do not contribute equally. Uniform processing leaves this distinction unexpressed in the architecture. We propose MARO, a Most-Recent Anchoring with Recurrent Ordering model that processes the look-back window from the most recent patch to the oldest. The most recent patch serves as the anchor. It initializes the latent state and conditions each subsequent step, so older patches are folded into a representation that remains centered on recent evidence. A single shared module is reused at every step, so extending the scan further into the past introduces no additional parameters. Intermediate states retained during the scan allow the forecast head to weigh short and long portions of the history separately. This expresses recency through the order of recurrent refinement. Extensive experiments across multiple real-world time series datasets show that MARO achieves state-of-the-art performance on both long-term and short-term forecasting tasks.Ablation studies examine the contribution of the main architectural components.

Abstract: Most long-term time-series forecasting models map the look-back window directly to the full horizon in a single pass. While efficient, this design does not explicitly identify which historical states are most relevant to different future segments or exploit what followed those states. Analog forecasting addresses this by retrieving past states similar to the present and using their observed continuations, but single nearest matches can be unreliable and overlapping patches may produce redundant candidates. We propose DuoTS, a Dual-Context Time Series forecasting model that uses retrieved evidence without relying on it exclusively. DuoTS first produces a base forecast with a parallel patch encoder and linear prediction head, then progressively refines it one future patch at a time. Each refinement combines two views: a current context that attends to recent tokens and captures the latest dynamics, and a detail context that provides distinct retrieved analogs together with their subsequent trajectories. Patch-wise refinement allows the model to balance these views across the forecast horizon and associate each future segment with evidence appropriate to its temporal distance from the present. Experiments on multiple real-world datasets show that DuoTS achieves state-of-the-art performance, while ablations confirm the contribution of each context. The refinement mechanism is also model-agnostic, requiring only an encoded look-back window and the future-patch position, and can therefore be integrated into existing forecasting models.

Abstract: Recent advances in deep learning for time series prediction have amplified the need for reliable uncertainty quantification. Conformal prediction has gained attention as a distribution-free framework for constructing prediction intervals with coverage guarantees. However, its coverage guarantees rely on data exchangeability, an assumption generally violated in time series. Active research has focused on developing conformal prediction methods for time series that overcome this limitation. While deep sequence models, such as recurrent neural networks and Transformers, have often been used in conformal prediction for time series, limited work has systematically studied how deep sequence models can be utilized in conformal prediction for time series. In this work, we systematically investigate the use of deep sequence models in conformal prediction for time series through three approaches: conditional quantile regression, conditional quantile function estimation, and localized conformal prediction. We provide a theoretical analysis establishing asymptotic conditional coverage guarantees for all three approaches under suitable assumptions. Through comprehensive experiments on real-world datasets, we demonstrate the effectiveness of leveraging deep sequence models into conformal prediction for time series.

Abstract: Real-world time series forecasting systems operate under non-stationary data streams, where forecasting performance may degrade over time. Although retraining can recover the performance, it incurs non-trivial computational and operational costs. Under limited deployment resources, the key challenge is therefore not only how to retrain but also when to retrain. While existing retraining policies often rely on indirect indicators such as drift alarms or model staleness, we instead use realized forecast errors as direct deployment feedback. In this paper, we propose PILOT (Pseudo-label-Informed Learned Online Trigger), an online retraining framework that learns when to retrain from forecast-error dynamics. Since ground-truth retraining labels are unavailable, PILOT constructs a pseudo-label from future increases in forecast error and trains a lightweight scorer to predict it from observed error states. At deployment, PILOT uses only completed forecast errors and serves as a plug-in module for arbitrary forecasting backbones without architectural modification. We evaluate PILOT under standard multivariate forecasting settings across eight benchmarks with three representative backbones---DLinear, iTransformer, and TimesNet. Across all three backbones, PILOT achieves state-of-the-art average-rank performance among retraining policies while maintaining a favorable performance--efficiency trade-off.

Abstract: Time Series Foundation Models (TSFMs) currently provide state-of-the-art results in forecasting tasks. They are available out-of-the-box and rely on in-context learning to make their predictions, which makes the quality of their performance highly sensitive to the user-selected lookback, covariates, horizon and training data distributions. In practise, the quality of the forecasts are variable but complementary, which highlights the need for a principled ensembling approach, rather than selecting the best context. This paper introduces Latent Inference-Time Guidance for TSFMs, which adaptively combines a pool of TSFM forecasts through a time-dependent latent space with independent components. The framework comes equipped with identifiability and reconstruction guarantees, whilst maintaining the off-the-shelf aspect of foundation models. We provide experiments on datasets at various frequencies and from multiple domains: these show that the approach is competitive with traditional ensembling approaches.

Abstract: Future exogenous variables provide valuable information for forecasting endogenous time series. Existing covariate-aware methods primarily learn the direct influence of exogenous variables on endogenous variables. However, these effects can be complex and change with the pattern of the exogenous variables, making them difficult to capture. Beyond this perspective, we observe that a given exogenous pattern often co-occurs with only a small set of endogenous response patterns. These associations motivate a strategy that matches future and historical exogenous patterns and uses the corresponding endogenous patterns to enhance forecasting. However, in real-world forecasting scenarios with multiple exogenous variables, each exogenous variable provides a distinct dimension for matching, creating a dilemma for this strategy between precise matching and sufficient historical support. To bridge this gap, we propose XMatch (EXogenous MATCHing), a covariate-aware forecasting model that realizes the aforementioned strategy through a tree-structured matching process that adaptively adjusts the number of exogenous variables used as matching conditions. Specifically, we first introduce the ProtoTree Creator, which organizes historical correspondences between exogenous and endogenous patterns into a ProtoTree, whose deeper levels incorporate additional exogenous variables for matching. For forecasting, we then design the ProtoTree Matcher, which uses future exogenous variables to query the ProtoTree and adaptively determines how many exogenous variables to use for matching based on exogenous pattern similarity and historical support. Finally, the matched endogenous patterns are used as explicit historical evidence to enhance forecasting. Extensive experiments on 12 real-world datasets demonstrate that XMatch outperforms state-of-the-art baselines.

Abstract: Real-world time series are inherently non-stationary, with trends, periodic patterns, and uncertainty evolving over time. While the Fourier domain offers a natural lens to model time series, current deep learning approaches do not explicitly model evolution and randomness in the Fourier spectra, which limits their ability to accurately predict both the expected trajectory and its uncertainty in non-stationary time series. Motivated by Evolutionary Spectra (ES) theory, we propose TimeES, a general framework that enables probabilistic and deterministic forecasting via the evolutionary spectra theory. Specifically, we derive a parameterizable evolutionary spectra formulation, recasting non-stationary random process modeling as learning an evolving representation modulated by random variables. Furthermore, we reduce the complexity of the estimated spectra from O(NM) to O(NK), where K << M/2, by exploiting Hermitian symmetry and spectral energy sparsity for frequency selection. Based on a simple linear backbone, our proposed TimeES achieves consistent state-of-the-art performance across both deterministic and probabilistic forecasting tasks, with high efficiency and interpretability. Code is available at: https://github.com/wwy155/TimeES.

Abstract: Cross-channel modeling is central to multivariate time-series forecasting, yet channels that are statistically related, predictively useful, and actually used by a trained forecaster are often treated as if they defined the same notion of importance. We show that they need not coincide. Cross-channel dependency structures change substantially across future offsets, and horizon-adaptive source selection improves a controlled Ridge predictor in 21 of 32 dataset--prediction-length conditions, with a mean gain of $5.16\%$. This selected-set signal also transfers to a matched nonlinear predictor. Yet imposing the same horizon-specific source logic on iTransformer yields only 11 of 20 wins and a mean gain of $0.208\%$, with little alignment between controlled and neural gains. Functional interventions further show that strong forecasters use cross-channel information, while their source-reliance rankings agree little with controlled utility or with one another across iTransformer, TimesNet, and a cross-channel TimeMixer. As a constructive consequence, bounded post-hoc support improves a frozen channel-independent forecaster in 12 of 16 dataset--horizon conditions, with a positive aggregate bootstrap interval. Cross-channel importance should therefore be interpreted relative to the forecasting mechanism and question that define it: related $\neq$ useful $\neq$ used.

Abstract: Time series out-of-distribution generalization requires forecasters to remain reliable when deployment dynamics differ from training conditions due to covariate shift, concept shift, and temporal dependence. Probably Approximately Correct Bayesian domain adaptation provides computable certificates by decomposing target risk into a source risk term, a source-to-target mismatch term, and a complexity term, but standard analyses rely on independent sampling and distributional stability, assumptions that are violated in time series by serial dependence and nonstationary shift. We propose a model-agnostic online martingale Probably Approximately Correct Bayesian framework that yields finite-sample certificates under temporal dependence and distribution shift. The certificate replaces independent-sample concentration with martingale concentration that adapts to loss scale and predictable variation. We use the certificate as a surrogate regularizer for online calibration by training a gated residual Bayesian head on top of a fixed forecasting backbone, producing a corrective update that reverts to the backbone prediction when the gate is closed. Online calibration combines a source risk anchor, a posterior-shift penalty, and a time-adaptive mismatch term computed from target windows observed before forecasting. It follows a predict-then-update protocol in which outcomes become available only after forecasting and are used to update subsequent predictions. Experiments across convolutional, attention-based, and large language model-based forecasters show improved stability and accuracy under covariate and concept shift.

Abstract: Completed multi-horizon forecasts provide residual feedback for a fixed forecaster, but retaining full residual blocks increases auxiliary state. We propose Endpoint-Preserving Online Correction (EPOC) with a compressed residual state. It stores low-order discrete cosine transform (DCT) coefficients and the final value of the preceding residual block. Within each channel, the endpoint is shared across component-wise online ridge regressions that also use current-forecast coefficients. The fitted DCT correction is blended with the base forecast. We evaluate eight multivariate series with DLinear and PatchTST, three seeds, and two training variants, yielding 96 matched fixed-base conditions at a 24-step horizon. EPOC achieves mean condition-wise reductions in mean squared error (MSE) and mean absolute error (MAE) of 15.40% and 9.35% from the uncorrected base, respectively, with a median of 6,352 B in retained auxiliary arrays. It has lower paired MSE than the $δ$-Adapter, COSA, FAC, and OMPB in a majority of conditions and uses less state than each. Full ELF achieves the largest mean MSE reduction, 19.29%, but its median retained state is 474,048 B ($\times$75 relative to EPOC). Equal-size summary controls favor the endpoint by 1.65--2.20% in paired MSE; a coefficient-reconstructed endpoint yields similar accuracy to the observed endpoint, highlighting its role as a shared input. Increasing the retained DCT component count from 4 to 8 adds 1.00 percentage point of MSE reduction for 5,728 B. On jointly trained bases, EPOC lowers MSE by 16.69--20.15% relative to globally blended TEFL-style adapters applied to the same base. The code and numerical records are available at https://github.com/keiotakmin/endpoint-preserving-residual-correction.

Abstract: We present $t_0$, a family of open-weights foundation models for forecasting with multivariate context. We release its first two members: $\texttt{t0-alpha}$ and $\texttt{t0-beta}$, respectively 102M and 256M parameters. Both condition their forecasts on target history, past covariates, and known-future covariates, without task-specific retraining. Their transformer layers alternate attention along time and across variates. They produce probabilistic forecasts through quantile predictions. Pretraining combines curated public data with synthetic generator families constructed to contain covariate-to-target dependencies. On GIFT-Eval, $\texttt{t0-alpha}$ reaches an aggregate CRPS of 0.4941, and $\texttt{t0-beta}$ a CRPS of 0.4738 and a MASE of 0.6865, third on both and within 4.0% of the best zero-shot TSFM. On fev-bench they score 42.2 and 46.7 in skill, the latter third again and 2.0 points behind the leader. We analyze $\texttt{t0-alpha}$ in depth. Known-future covariates raise its skill by 6.3 percentage points across 30 tasks. The report also examines its calibration, its rollout strategy on long horizons, and its robustness to missing data. On the Victoria electricity-demand benchmark, $\texttt{t0-beta}$ is among the most accurate models with a context of nearly a year. In an independent Macrocosm evaluation of hourly ERCOT prices over 29 months, both cut the MAE of the lagged-price baseline by 38%.

Abstract: Long-term time series forecasting has made significant progress by leveraging multi-scale information to capture hierarchical temporal patterns and model long-range dependencies. However, temporal downsampling in existing multi-scale methods inevitably smooths detailed temporal fluctuations, and this information loss is further aggravated by their emphasis on dominant trends across scales, resulting in insufficiently expressive representations. To address this, we propose a Multi-Scale Wavelet Mixing (MWMixer) model, which incorporates a Bidirectional Frequency-Bands Mixing strategy to recover lost temporal details across scales, enabling complementary cross-scale information interactions. Then, a Dynamic Scale-Adaptive Fusion module learns time-varying weights for each scale to fuse multi-scale forecasts into the final prediction, enhancing the flexibility of multi-scale aggregation. In addition, a cross-scale consistency loss aligns each coarse-scale prediction with the interval-averaged fine-scale outputs, while a multi-scale supervision loss enforces prediction accuracy at each scale, promoting consistent learning across scales. Extensive experiments on seven real-world datasets demonstrate that MWMixer achieves competitive performance in long-term forecasting.

Abstract: Text-controlled time series generation aims to synthesize sequences that follow natural-language descriptions while remaining faithful to real data distributions. Existing paradigms often couple semantic understanding and sequence modeling in a single continuous latent space, lacking explicit local semantic anchors and separation between global continuous attributes and local discrete shapes. As a result, key local structures may be smoothed, missed, or misplaced. We propose Shape Lexicon (ShapeLex), which decouples text-to-sequence generation into discrete symbolization of local shapes and continuous modeling of global attributes. ShapeLex first induces a reusable vocabulary of discrete shape units, such as rises, spikes, and sharp drops, from training data, forming an interpretable symbolic space. An autoregressive generator then selects shapes according to the textual description, adjusts attributes such as position and duration, and composes them in temporal order into a shape skeleton. Finally, a mixture-density scale head models and samples the overall level and volatility to restore realistic global scale. Experiments on twelve public datasets, real user-written text, and downstream forecasting tasks show that ShapeLex generates series that better match real data distributions than existing methods. In addition, paired supervision is automatically synthesized from the learned vocabulary, avoiding annotation costs that grow with dataset size and improving scalability.

Abstract: Probabilistic forecasting requires accurate central predictions and calibrated uncertainty estimates. This paper presents TEMPER, the Temporal Encoder-Masked Probabilistic Ensemble Regressor, a univariate time-series forecasting algorithm that combines a temporal autoencoder, a differentiable masked neural decision forest, continuous ranked probability score (CRPS) training, and Gaussian-mixture post-processing. The R implementation is built on torch for R and returns horizon-wise density, distribution, quantile, and sampler functions. We evaluate TEMPER on three deterministic synthetic level series with trend, periodic, regime-switching, nonlinear-threshold, and heteroskedastic components. Across 96 rolling-origin forecasts at horizons t + 1, t + 5, t + 20, and t + 60, TEMPER obtains 2.824% mean CRPS normalized by origin level, 3.635% median absolute error, and 68.8% empirical 90% interval coverage after training with a 300-epoch cap and early-stopping patience of 100. A naive persistence bootstrap has the best aggregate CRPS, 2.763%, while TEMPER has the best median absolute error and the best CRPS at t+1 and t+5. The ablation study uses matched series-origin-horizon cells, horizon-wise CRPS deltas, endpoint sensitivity summaries, and a calibration-specific interval study. Relaxing the learned mask improves average CRPS by 0.472 percentage points on the ablation subset, mainly through long-horizon gains. A twofold interval inflation improves held-out coverage from 54.2% to 91.7% and gives the best 90% interval score among tested calibration rules. The results identify calibration, horizon-specific tuning, and component selection as the central research priorities.

Abstract: Direct forecasting has become a standard paradigm for multivariate time-series forecasting because it predicts the full future horizon in a single pass. However, its training objective is often still decomposed into pointwise errors such as MSE. Such objectives provide stable supervision, but they do not explicitly preserve the structure of the future trajectory: temporal coherence within each variable and relational consistency across variables can both be weakened. We propose CoRe, a model-agnostic learning objective for direct multivariate forecasting. CoRe replaces pointwise supervision with two output-space constraints: a frequency coherence loss that aligns predicted and target spectra, and a low-rank relational graph loss that matches sampled pairwise differences in a target-derived PCA subspace. The resulting objective introduces no trainable parameters and can be applied to existing forecasting backbones by changing only the loss. Experiments on standard benchmarks show that CoRe improves strong baselines, compares favorably with recent forecasting objectives, and remains effective across different backbones, datasets, and hyperparameter settings overall consistently.

Abstract: Recent advances in explaining time series (TS) models have produced methods that identify which past values a prediction depends on. However, most existing methods return a single importance vector, assuming that every predicted step depends on the same past values. In this paper, we show that this assumption does not hold, as different forecast steps depend on different past values. Motivated by this observation, we propose Horizon-Resolved eXplanation (HRX), which adds a horizon axis to the explanation, so that every forecast step receives its own importance map. HRX is a simple yet effective plug-in framework with three components: 1) an estimator that reads these maps out of any differentiable forecaster without modifying the TS backbone, 2) an evaluation protocol that validates the horizon axis by measuring how much a single forecast step changes when the inputs an importance map ranks highest are removed, and 3) a rank criterion that predicts in advance whether the axis is worth resolving on a given TS. We further show that this step-wise dependence is low-dimensional, as the explanations of all steps are built from a few shared maps whose number does not grow with the forecast length. Extensive experiments across various backbones and datasets show that the improvement comes from the horizon axis and holds for estimators of previous explanation methods. Code is available at https://github.com/seunghan96/HRX.