Times series foundation models (TSFMs) have emerged as a promising paradigm for time series analyses and forecasting, showing remarkable generalization performance across different domains. Despite the efforts made on hallucinations of foundation models, hallucinations of TSFMs have been underexplored in existing literature. In this paper, we formally define TSFM hallucinations in the zero-shot forecasting setting by examining whether a generated forecast exhibits different dynamics from those of the context. Our study reveals that TSFM hallucinations are associated with the loss of context information in hidden states during forward propagation. As such, we propose a methodology to identify signal subspaces of TSFMs and magnify the information through intervention. Experiments demonstrate that our proposed intervention approach effectively mitigates hallucinations and improves forecasting performance. The signal strength measure computed from signal subspaces shows strong predictive power of hallucinations and forecasting performance of the model. Our work contributes to deeper understanding of TSFM trustworthiness that could foster future research in this direction.

Online portfolio selection seeks to determine a sequence of allocations to maximize capital growth. Classical universal strategies asymptotically match the best constant-rebalanced portfolio but ignore potential forecasts, whereas heuristic methods often collapse when belief fails. We formalize this tension in a learningaugmented setting in which an investor observes (possibly erroneous) predictions prior to each decision moment, and we introduce the Rebalanced Arithmetic Mean portfolio with predictions (RAM). Under arbitrary return sequences, we prove that RAM captures at least a constant fraction of the hindsight-optimal wealth when forecasts are perfect while still exceeding the geometric mean of the sequence even when the predictions are adversarial. Comprehensive experiments on largescale equity data strengthen our theory, spanning both synthetic prediction streams and production-grade machine-learning models. RAM advantages over universalportfolio variants equipped with side information across various regimes. These results demonstrate that modest predictive power can be reliably converted into tangible gains without sacrificing worst-case guarantees.

We introduce TOTO, a time series forecasting foundation model with 151 million parameters. TOTO uses a modern decoder-only architecture coupled with architectural innovations designed to account for specific challenges found in multivariate observability time series data. TOTO's pre-training corpus is a mixture of observability data, open datasets, and synthetic data, and is 4-10 larger than those of leading time series foundation models. Additionally, we introduce BOOM, a large-scale benchmark consisting of 350 million observations across 2,807 real-world time series. For both TOTO and BOOM, we source observability data exclusively from Datadog's own telemetry and internal observability metrics. Extensive evaluations demonstrate that TOTO achieves state-of-the-art performance on both BOOM and on established general purpose time series forecasting benchmarks.

Accurate, high-resolution ocean forecasting is crucial for maritime operations and environmental monitoring. While traditional numerical models are capable of producing sub-daily, eddy-resolving forecasts, they are computationally intensive and face challenges in maintaining accuracy at fine spatial and temporal scales. In contrast, recent data-driven approaches offer improved computational efficiency and emerging potential, yet typically operate at daily resolution and struggle with sub-daily predictions due to error accumulation over time. We introduce FuXiOcean, the first data-driven global ocean forecasting model achieving six-hourly predictions at eddy-resolving 1/12 spatial resolution, reaching depths of up to 1500 meters. The model architecture integrates a context-aware feature extraction module with a predictive network employing stacked attention blocks. The core innovation is the Mixture-of-Time (MoT) module, which adaptively integrates predictions from multiple temporal contexts by learning variable-specific reliability, mitigating cumulative errors in sequential forecasting. Through comprehensive experimental evaluation, FuXi-Ocean demonstrates superior skill in predicting key variables, including temperature, salinity, and currents, across multiple depths.

Performative predictions are forecasts which influence the outcomes they aim to predict, undermining the existence of correct forecasts and standard methods of elicitation and estimation. We show that conditioning forecasts on covariates that separate them from the outcome renders the target distribution forecast-invariant, guaranteeing well-posedness of the forecasting problem. However, even under this condition, classical proper scoring rules fail to elicit correct forecasts. We prove a general impossibility result and identify two solutions: (i) in decision-theoretic settings, elicitation of correct and incentive-compatible forecasts is possible if forecasts are separating; (ii) scoring with unbiased estimates of the divergence between the forecast and the induced distribution of the target variable yields correct forecasts. Applying these insights to parameter estimation, conditional forecasts and proper scoring rules enable performatively stable estimation of performatively correct parameters, resolving the issues raised by Perdomo et al. (2020). Our results expose fundamental limits of classical forecast evaluation and offer new tools for reliable and accurate forecasting in performative settings.

Diffusion models are a powerful tool for probabilistic forecasting, yet most applications in high-dimensional complex systems predict future states individually. This approach struggles to model complex temporal dependencies and fails to explicitly account for the progressive growth of uncertainty inherent to the systems. While rolling diffusion frameworks, which apply increasing noise to forecasts at longer lead times, have been proposed to address this, their integration with state-of-the-art, high-fidelity diffusion techniques remains a significant challenge. We tackle this problem by introducing Elucidated Rolling Diffusion Models (ERDM), the first framework to successfully unify a rolling forecast structure with the principled, performant design of Elucidated Diffusion Models (EDM). To do this, we adapt the core EDM components-its noise schedule, network preconditioning, and Heun sampler-to the rolling forecast setting. The success of this integration is driven by three key contributions: piq a novel loss weighting scheme that focuses model capacity on the mid-range forecast horizons where determinism gives way to stochasticity; piiq an efficient initialization strategy using a pre-trained EDM for the initial window; and piiiq a bespoke hybrid sequence architecture for robust spatiotemporal feature extraction under progressive denoising. On 2DNavier-Stokes simulations and ERA5 global weather forecasting at 1.5 resolution, ERDM consistently outperforms key diffusion-based baselines, including conditional autoregressive EDM. ERDM offers a flexible and powerful general framework for tackling diffusion-based dynamics forecasting problems where modeling uncertainty propagation is paramount.1

Online portfolio selection seeks to determine a sequence of allocations to maximize capital growth. Classical universal strategies asymptotically match the best constant-rebalanced portfolio but ignore potential forecasts, whereas heuristic methods often collapse when belief fails. We formalize this tension in a learning-augmented setting in which an investor observes (possibly erroneous) predictions prior to each decision moment, and we introduce the Rebalanced Arithmetic Mean portfolio with predictions (RAM). Under arbitrary return sequences, we prove that RAM captures at least a constant fraction of the hindsight-optimal wealth when forecasts are perfect while still exceeding the geometric mean of the sequence even when the predictions are adversarial. Comprehensive experiments on large-scale equity data strengthen our theory, spanning both synthetic prediction streams and production-grade machine-learning models. RAM advantages over universal-portfolio variants equipped with side information across various regimes. These results demonstrate that modest predictive power can be reliably converted into tangible gains without sacrificing worst-case guarantees.

Time series forecasting plays a pivotal role in various real-world applications and has attracted significant attention in recent decades. While recent methods have achieved remarkable accuracy by incorporating advanced inductive biases and training strategies, we observe that instance-level variations remain a significant challenge. These variations--stemming from distribution shifts, missing data, and long-tail patterns--often lead to suboptimal forecasts for specific instances, even when overall performance appears strong. To address this issue, we propose a model-agnostic framework, PIR, designed to enhance forecasting performance through Post-forecasting Identification and Revision. Specifically, PIR first identifies biased forecast instances by estimating their predictive accuracy. Based on this, the framework revises the forecasts using contextual information, including covariates and historical time series, from both local and global perspectives in a post-processing fashion. Extensive experiments on real-world datasets with mainstream forecasting models demonstrate that PIR effectively mitigates instance-level errors and significantly improves forecasting reliability.

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters (0.1%) and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, . We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

The use of residential photovoltaics has increased dramatically in recent years. With battery systems becoming more affordable, the optimal operation of a photovoltaic-battery system can bring significant savings to households. Optimal control requires correct forecasts of underlying parameters, such as photovoltaic power generation, to schedule the battery. While forecasting models have become increasingly accurate due to algorithmic advances and data availability, accuracy is typically measured in generic metrics which might not align with the downstream application. This study proposes a decision-focused learning framework that integrates optimization and prediction by training a Long Short-Term Memory photovoltaic energy forecaster on the downstream optimal scheduling of a battery system. The proposed methodology is compared against a standard two-phase approach. Across a 14-month evaluation period, the decision-focused method reduced average electricity costs across twenty buildings by 3.6% when normalized against performance bounds defined by a perfect forecast and a baseline of no optimization. Critically, this financial improvement was achieved despite the model exhibiting a root mean squared error of 19.9%, significantly higher than the decoupled model's 8.2%. Warm-starting the decision-focused model further improves results, lowering average cost by approximately 8%, while also mitigating the negative impact on statistical accuracy (root mean squared error of 13.7%). The findings are statistically significant at the 0.001 level across the twenty households and for each household individually. These results demonstrate that aligning forecast models with optimization goals is key for achieving cost advantages in PV-battery systems. Future research should replicate these findings on other datasets, alternate forecasting models and alternate optimization algorithms.