Exogenous Time Series Forecasting

Accurate real-time forecasting of atmospheric pollutants is essential for reducing exposure risks and improving public health. Traditional numerical forecasting systems suffer from incomplete parameterizations, uncertain inputs, and high computational cost. Existing deep learning approaches improve efficiency, but often entangle meteorological and pollutant variables within unified forecasting frameworks, limiting flexibility and pollutant-specific representation learning. To address these challenges, we propose AirMPA, a decoupled autoregressive framework for meteorology-to-pollution forecasting. AirMPA predicts 13 atmospheric pollutants at 0.4° spatial resolution and 12-h temporal resolution using meteorological fields, emission priors, and historical pollutant concentrations. The model is built on an improved Swin-Transformer architecture with zonal release attention and dual-branch fusion, enabling more effective modeling of global transport continuity and heterogeneous pollutant dynamics. During training, AirMPA uses the fifth-generation atmospheric reanalysis from the European Centre for Medium-Range Weather Forecasts (ERA5) as meteorological forcing, while during inference it directly ingests forecast fields from external meteorological models, enabling stable autoregressive prediction up to 5 days ahead. Experiments show that AirMPA consistently outperforms Aurora and surpasses the Copernicus Atmosphere Monitoring Service (CAMS) in approximately 90% of pollutant-lead-time evaluation cases over the 5-day forecast horizon, while outperforming CAMS on all variables beyond 48 h. These results demonstrate the potential of decoupled meteorology-to-pollution forecasting for global air quality prediction.

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/.

We release Ride-Hailing, a large-scale ride-hailing time series dataset synthesized from DiDi's marketplace data across 200 spatial areas. Ride-Hailing spans four consecutive years at half-hourly granularity and covers three representative exogenous scenarios: Weather Disturbance, Holiday Effect, and Large-scale Event Impact. Built upon Ride-Hailing, we introduce RideBench, a comprehensive benchmark for exogenous-aware ride-hailing forecasting, covering both regular week-ahead forecasting and long-horizon 8-week-ahead forecasting with up to 2,688 prediction steps. RideBench evaluates over 30 representative forecasting methods, including endogenous-only models, exogenous-aware models, and time series foundation models. Our results show that future-known exogenous variables provide clear benefits in regular week-ahead forecasting, especially under weather, holiday, and large-scale event (e.g., major sporting events and concerts) scenarios. However, current exogenous-aware models still struggle to fully capture disturbance-induced pattern changes under complex external contexts. For long-horizon forecasting, existing models cannot simultaneously achieve low pointwise errors, accurate broad trends, and reliable near-term forecasts. These findings reveal a clear mismatch between existing forecasting models and real-world ride-hailing requirements, highlighting the need for models that can better exploit future-known exogenous information, scale across heterogeneous areas, and support long-horizon planning. By introducing Ride-Hailing and RideBench, we aim to encourage the community to study these practical challenges in real-world ride-hailing forecasting.

Real-world time series are frequently driven by exogenous events and structural shifts, rendering conventional forecasting based solely on historical numerical observations insufficient. While language models can retrieve external news, standard retrieval-augmented approaches struggle with high noise, missing signals, and an inability to reason causally about event impacts. We propose SEER (Self-Evolving Event Reasoning and Retrieval), a closed-loop framework that dynamically optimizes event conditioning for time series forecasting. SEER translates prediction errors into two decoupled feedback mechanisms: (i) a reflective retrieval memory that refines subsequent search queries and filters spurious noise, and (ii) a persistent causal knowledge base that distills transferable domain dynamics. SEER enforces strict chronological boundaries across both event retrieval and reflection, preventing look-ahead bias and data leakage. Across six volatile time-series benchmarks, SEER consistently outperforms state-of-the-art time series foundation models and language model baselines.

Despite the success of Time Series Foundation Models (TSFMs) on broad benchmarks, their ability to internalize basic temporal logic, especially in settings supported by exogenous covariates, remains under-examined. We introduce SimpleTimeBench, a diagnostic univariate and multivariate "unit test" suite for primitives such as monotonic trends, periodic signals and leading indicator covariates, scenarios where near-perfect forecasts should be trivial. Surprisingly, prominent multivariate TSFMs (Chronos-2, Moirai and Toto) frequently produce suboptimal zero-shot forecasts for these inputs. While fine-tuning Chronos-2 improves its behaviour on specific tasks, we show that this adaptation degrades performance on other fundamental patterns rather than enhancing its generalizable foundational capabilities. This reveals a gap between pre-training scale and basic temporal reasoning, suggesting that current TSFMs could potentially lack the inductive biases needed to capture simple predictable functions. We further demonstrate that these failures are not merely synthetic curiosities: they persist in real-world sensor forecasting, where TSFMs consistently underutilize leading indicators available in observed covariates. This inability to capture simple relationships limits the practical utility and reliability of current multivariate models.

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%.

Modern power systems are growing increasingly complex as they integrate diverse generation sources to meet rising demand, making accurate load forecasting challenging. Recent advances in time-series foundation models (TSFMs) resulted in promising performance in zero-shot univariate load forecasting tasks. However, real-world load forecasting often involves multiple target variables and requires the integration of exogenous variables, raising important questions about the utility of TSFMs in realistic settings. In this study, we position Chronos-2, a recently developed model by Amazon, as a representative multi-channel TSFM that supports univariate, multivariate, and covariate-informed forecasting, and conduct a systematic investigation of how such models can be used for real-world load forecasting. While prior work has evaluated Chronos-2 on a limited number of energy-related tasks in a zero-shot setting, its performance relative to established task-specific deep learning models and its behavior when adapted using task-specific historical data remains insufficiently understood. In this work, we evaluate Chronos-2 on two real-world utility datasets, ISO New England and ENTSO-E, and benchmark it against widely used task-specific deep learning models. Our results show that Chronos-2 benefits substantially from task-specific fine-tuning and achieves strong short-horizon forecasting performance, but its zero-shot accuracy lags behind task-specific models and its forecasting error grows more rapidly with increasing forecast steps. Overall, this study provides a detailed characterization of the strengths and limitations of TSFMs such as Chronos-2 in grid load forecasting and offers practical insights into how a pretrained TSFM can be effectively adapted for operational load forecasting applications.

Accurate forecasting of cellular network traffic is essential for network planning, resource allocation, and quality-of-service assurance in modern mobile communication systems. Real-world traffic often exhibits bursty endogenous dynamics and disturbances triggered by external urban events, which makes reliable prediction highly challenging. Most existing spatiotemporal traffic forecasting methods primarily focus on intrinsic traffic patterns or structural relationships within a single modality, and rarely model burst behavior together with exogenous contextual signals. To address this issue, we propose MSPF-Net, a multimodal cellular traffic forecasting framework that integrates external contextual information. Specifically, MSPF-Net consists of a Spatiotemporal-Frequency Traffic Encoder for capturing temporal, spatial, and spectral traffic patterns, a Peak Enhancement Module for extracting burst-aware representations of sudden spikes, a News Context Representation Module for encoding urban news streams into exogenous contextual embeddings, and a Dynamic Fusion Prediction Module for adaptively integrating these heterogeneous signals to generate forecasts. Experiments on the Milano, Trento, and LTE traffic datasets demonstrate that jointly modeling traffic dynamics, burst patterns, and news contextual signals can effectively improve forecasting performance.

Time series forecasters that use exogenous covariates are fragile in deployment: when those covariates are noised, temporally misaligned, or missing, strong exogenous-fusion and exogenous-adapted models can degrade far above the endogenous-only floor. We study whether such robustness requires specialized architectures, or whether it can be obtained through a simple training intervention. We propose exogenous dropout, a model-agnostic method that randomly zeros whole exogenous channels during training. Across electricity-price forecasting, reservoir hydrology, and meteorology, exogenous dropout substantially improves robustness under Gaussian noise, temporal misalignment, and fully missing channels, while preserving clean accuracy. Applied to a dual-correlation network, it yields the most robust model in our experiments, outperforming a deliberately strong bounded architectural foil, BoundEx, which combines a learnable gate, a fallback residual to the endogenous backbone, and per-channel exogenous FiLM modulation. Architecture-by-dropout ablations, gate-behavior diagnostics, and a representation-level bound show that explicit architectural boundedness is not necessary for this robustness: an unbounded model trained with exogenous dropout is more robust than the bounded model in every domain. We release a corruption-robustness benchmark and recommend exogenous dropout as a simple, strong baseline for future work on time series forecasting with covariates.

Medical and public health experts must make real-time resource decisions, such as expanding hospital bed capacity, based on projected hospitalization trends during large-scale healthcare disruptions (e.g., operational failures or pandemics). Forecasting models can assist in this task by analyzing large volumes of resource-related data at the facility level, but they must be reliable for decision-making under real-world data conditions. Recent work shows that large language models (LLMs) can incorporate richer forms of context into numerical forecasting. Whereas traditional models rely primarily on temporal context (i.e., past observations), LLMs can also leverage non-temporal public health context such as demographic, geographic, and population-level features. However, it remains unclear how these models should be used to produce stable or decision-relevant predictions in real-world healthcare settings. To evaluate how LLMs can be effectively used in this setting, we evaluate three approaches across 60 counties with low-,mid-, and high-hospitalization intensities in the United States: direct LLM-based forecasting, classical time-series models, and a context-augmented hybrid pipeline (HybridARX) that incorporates LLM-derived signals into structured models. Because the goal is operational decision-making rather than error minimization alone, we evaluate performance with bias and lead-lag alignment in addition to standard forecasting metrics. Our results show that HybridARX improves over classical ARX by yielding more stable and better-calibrated forecasts, particularly when incorporating noisy contextual signals into structured time-series models. These findings suggest that, in non-stationary healthcare resource forecasting, LLMs are most useful when embedded within structured hybrid models.

In many time series forecasting settings, the target time series is accompanied by exogenous covariates, such as promotions and prices in retail demand; temperature in energy load; calendar and holiday indicators for traffic or sales; and grid load or fuel costs in electricity pricing. Ignoring these exogenous signals can substantially degrade forecasting accuracy, particularly when they drive spikes, discontinuities, or regime and phase changes in the target series. Most current time series foundation models (e.g., Chronos, Sundial, TimesFM, TimeMoE, TimeLLM, and LagLlama) ignore exogenous covariates and make forecasts solely from the numerical time series history, thereby limiting their performance. In this paper, we develop ApolloPFN, a prior-data fitted network (PFN) that is time-aware (unlike prior PFNs) and that natively incorporates exogenous covariates (unlike prior univariate forecasters). Our design introduces two major advances: (i) a synthetic data generation framework that injects realistic temporal patterns, structural changes, and exogenous dependencies into the PFN prior; and (ii) time-aware architectural modifications that embed inductive biases needed to exploit temporal context. We demonstrate that ApolloPFN outperforms existing baselines across several forecasting benchmarks with exogenous information, including M5, electric price forecasting, UCI Air Quality, and Solar Energy datasets.

Exogenous variables offer valuable supplementary information for predicting future endogenous variables. Forecasting with exogenous variables needs to consider both past-to-future dependencies (i.e., temporal correlations) and the influence of exogenous variables on endogenous variables (i.e., channel correlations). This is pivotal when future exogenous variables are available, because they may directly affect the future endogenous variables. Many methods have been proposed for time series forecasting with exogenous variables, focusing on modeling temporal and channel correlations. However, most of them use a two-step strategy, modeling temporal and channel correlations separately, which limits their ability to capture joint correlations across time and channels. Furthermore, in real-world scenarios, time series are frequently affected by various forms of noises, underscoring the critical importance of robustness in such correlations modeling. To address these limitations, we propose GCGNet, a Graph-Consistent Generative Network for time series forecasting with exogenous variables. Specifically, GCGNet first employs a Variational Generator to produce coarse predictions. A Graph Structure Aligner then further guides it by evaluating the consistency between the generated and true correlations, where the correlations are represented as graphs, and are robust to noises. Finally, a Graph Refiner is proposed to refine the predictions to prevent degeneration and improve accuracy. Extensive experiments on 12 real-world datasets demonstrate that GCGNet outperforms state-of-the-art baselines.

Time series forecasting has witnessed an increasing demand across diverse industrial applications, where accurate predictions are pivotal for informed decision-making. Beyond numerical time series data, reliable forecasting in practical scenarios requires integrating diverse exogenous factors. Such exogenous information is often multi-dimensional or even multimodal, introducing heterogeneous interactions that unimodal time series models struggle to capture. In this paper, we delve into an aviation maintenance scenario and identify three distinct types of exogenous factors that influence temporal dynamics through distinct interaction modes. Based on this empirical insight, we propose Aura, a universal framework that explicitly organizes and encodes heterogeneous external information according to its interaction mode with the target time series. Specifically, Aura utilizes a tailored tripartite encoding mechanism to embed heterogeneous features into well-established time series models, ensuring seamless integration of non-sequential context. Extensive experiments on a large-scale, three-year industrial dataset from China Southern Airlines, covering the Boeing 777 and Airbus A320 fleets, demonstrate that Aura consistently achieves state-of-the-art performance across all baselines and exhibits superior adaptability. Our findings highlight Aura's potential as a general-purpose enhancement for aviation safety and reliability.

While generative modeling facilitates probabilistic time series forecasting, incorporating heterogeneous exogenous information remains challenging. Diffusion Transformers (DiT) provide a scalable framework for conditional generation, yet their adaptation to forecasting calls for conditioning mechanisms tailored to time series. Endogenous targets and exogenous covariates differ in sources, semantics, and statistical characteristics, while sharing temporal coordinates that support fine-grained conditional guidance. Covariates can describe future variability and temporal dependence beyond the conditional mean targeted by direct regression. Motivated by these considerations, we propose Diffusion Transformers for Time Series (DiTS), a Multimodal Diffusion Transformer for covariate-aware forecasting. DiTS models endogenous targets and exogenous covariates as distinct modalities, jointly conditioning future generation on target history and available covariates. Flow matching makes covariate-dependent distributional information relevant to velocity prediction conditioned on noisy future states. We introduce Time-aligned Modulation, extending AdaLN with the temporal-alignment prior to generate patch-wise modulation parameters from aligned covariates and diffusion time. Across diverse covariate-aware forecasting tasks, DiTS achieves strong performance in both deterministic and probabilistic forecasting, demonstrating the effectiveness of conditional generation for both point and distributional forecasting.