Robust Time Series Forecasting

In time-series forecasting tasks, the use of recursive forecasting on high-dimensional data substantially increases the complexity of the prediction process. The main challenge is that long-term dynamics becomes harder to model, since the sequences show greater temporal variability. To counteract this limitation and improve the modeling of long-term dynamics, and more importantly, address high-dimensional recursive forecasting, this paper uses a Wasserstein GAN equipped with a progressive Lipschitz penalty and an adaptive kernel. This model is capable of taking a window of the data stream and forecasting the next values, subsequently reconstructing the time-series stream and dynamically adapting its kernel to each new window. The proposed model is a deep learning framework based on a Wasserstein GAN (WGAN-CLP) with an adaptive kernel to model alterations in streaming voltage time series. To establish the methodological foundation, we review the WGAN-LP formulation another variant model in this class and extend its framework through an adaptive kernel critic model. We then evaluate this extended model using power ratios, correlation coefficient (CC), and relative root mean squared error (RRMSE). The experimental results demonstrate that the proposed model outperforms benchmark methods in both accuracy and robustness. The evaluation shows promising performance of the WGAN-CLP with an adaptive kernel framework in forecasting sequence alterations across the voltage and energy time-series datasets.

Long-term time series forecasting (LTSF) models predominantly employ patch-based encoders terminated by a flatten readout head that maps the entire encoded historical memory to all future steps through a single shared projection. This implicit coupling of future positions obscures position-specific historical-to-future alignment and amplifies sensitivity to corrupted inputs and extreme supervision noise. We present SACQ, a plug-in structured prediction head that replaces flatten readout while keeping the encoder unchanged. SACQ adopts a two-stage decoding pipeline: it first establishes a coarse patch-grid forecast scaffold, then refines each future position through cross-attention over historical memory and merges the attention-derived correction with the coarse scaffold via a learned per-patch gate. To stabilize optimization under long horizons and noisy labels, we further propose a batch-adaptive scaled log-cosh loss that automatically calibrates robustness to the current residual scale, suppressing outlier gradients while preserving MSE-like sensitivity for typical errors. SACQ attains top-tier test MSE/MAE across PatchTST, DLinear, and patch-Mamba backbones with only modest incremental overhead in parameters and latency. Under inference-time input corruption and training-set label-noise stress tests, SACQ substantially outperforms flatten readouts, with ablation studies validating each architectural component.

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.

Time series forecasting (TSF) increasingly drives decisions in transportation, energy, finance, healthcare, and infrastructure, yet current evaluation remains overly narrow: standard benchmarks reward low held-out error, while robustness studies typically reduce failure to Gaussian noise, random masking, or bounded adversarial perturbations. This obscures the real failure modes of deployed forecasting systems. Input-side anomalies are not merely noisier inputs: they often reflect structured events that alter temporal dynamics, break cross-variable dependencies, induce regime shifts, or propagate from faulty sensors to downstream decisions. These semantic, causal, and system-level failures cannot be faithfully captured by i.i.d. perturbations alone. The rise of TSF foundation models makes this evaluation gap more urgent, as unauditable pretraining corpora make held-out generalization increasingly unreliable. We therefore advocate scenario-grounded stress testing. Each test instance should include historical inputs and future targets, together with a semantic scenario, an explicit failure operator, and a measurable difficulty level. This shift makes evaluation interpretable, attributable, and deployment-relevant and friendly, enabling the community to ask not only which model is accurate, but under what conditions it fails and why.

Time series forecasting underpins critical decision-making across diverse domains. While large language models (LLMs) offer promising reasoning capabilities, existing LLM-based time series forecasting approaches either reduce them to numerical predictors that bypass their strengths, or allow direct forecast generation that destabilizes predictions in non-stationary settings. We introduce CTRL, a framework that decouples semantic reasoning from quantitative prediction. A frozen backbone generates base forecasts, while specialized LLM agents function as controllers that analyze backbone prediction errors through decomposed trend, seasonal, and irregular components, grounding reasoning in interpretable temporal structure. Each agent outputs compact control signals that a lightweight residual decoder translates into forecast corrections. CTRL incorporates label-free test-time adaptation that detects distribution shift from input statistics alone and readapts control signals with only 3-24 LLM calls via caching. CTRL is explicitly designed to improve robustness under non-stationary temporal dynamics and distribution shift, while remaining competitive on highly stationary time series where adaptive correction provides limited additional benefit.

Average squared error cannot reveal whether forecasting performance degrades because the future becomes less predictable or because forecasts move farther from the conditional mean. We introduce paired, mechanism-controlled stress tests that decompose changes in expected squared error at each lead time into environmental risk and forecast-oracle distance, using an origin-conditioned predictive oracle unavailable to the evaluated models. Three end-to-end controls have known attribution. Specifically, the null, environmental-only, and information-gap controls verify that the pipeline assigns changes to the correct component. We then apply the benchmark to 24 deployable forecasters. Under frequent switching, 14 methods have higher realized MSE but lower oracle distance; under outlier-variance feedback, 19 have higher MSE but lower scale-standardized MSE. Short- and long-lead stress-response rankings have Spearman correlation 0.624, revealing substantial horizon-dependent reordering. We then study multivariate relation shifts. Across six models and three coupling severities, oracle distance accounts for only 0.7-3.9% of the decomposed expected-risk increase, and environmental-risk majority persists in an eight-channel system and a matched-difficulty audit of Ring, Block, and Hub relations. Finally, prespecified contrasts on independent data-generating process (DGP) realizations show that several visually compelling discovery profiles, including trend accumulation and the hypothesized switching reversal, do not replicate. The benchmark thus combines component-wise diagnosis with a held-out stability audit. It complements real-data out-of-distribution evaluation, which measures performance under realistic shifts when exact oracle attribution is unavailable.

Retrieval-augmented generation (RAG) complements parametric models with retrieved external evidence. The same idea is attractive for continuous-output regression, but directly reusing retrieved target values is often not robust when samples differ in output level, numerical scale, or local dynamics. Moreover, conventional forecasting pipelines generally use residuals for model optimization and error diagnosis, but do not retain individual historical residual examples as memory that can be accessed at inference time.For multivariate time-series forecasting, we propose RATL, a plug-in residual-retrieval and feedback-correction method. RATL freezes a base forecaster to construct retrieval keys and turns its historical forecast residuals into a train-only memory specific to that base model. At inference time, RATL retrieves residual trajectories from similar historical contexts subject to causal availability constraints, then uses a set-aware router operating over forecast blocks and variables to select and combine these trajectories. Experiments show that historical residuals matched to the current context contain reusable forecasting information and that RATL improves frozen base forecasters in most experimental settings. Ablations further show that learned routing strengthens raw residual feedback, while validation-based correction-strength selection limits residual over-injection.On real-world benchmarks, we use iTransformer as the primary frozen base forecaster, compare against multiple strong forecasting baselines, and test transferability across backbones. The results show that RATL can further improve base-forecaster performance in most settings.Overall, RATL shifts the retrieved object from historical target values to base-model-specific historical forecast errors, providing a plug-in, residual-memory-based paradigm for learned feedback correction in continuous-output forecasting.

Probabilistic multivariate time series (MTS) forecasting is crucial for modeling complex dynamical systems. However, existing diffusion-based methods rely on task-specific conditional paradigms that lack flexibility and struggle with inherent "information heterogeneity"--the significantly varying noise levels and evolutionary patterns across variables. To address this, we propose DynG-Diff, a variable-sensitive dynamic guidance diffusion framework for probabilistic multivariate time-series forecasting: (1) DynG-Diff adopts a two-stage separated training strategy and uses an unconditional diffusion backbone to model the joint distribution of multivariate time series. (2) DynG-Diff introduces a lightweight state-aware policy network that adaptively infers variable reliability from real-time noisy states and one-step denoising estimates, outputting a dynamic guidance strength matrix. (3) DynG-Diff mathematically formulates this dynamic weight as the local precision of the observation distribution, enabling precise guidance for high-confidence variables during inference while filtering out interference from anomalous noise. Extensive experiments on real-world benchmarks demonstrate competitive probabilistic forecasting performance against state-of-the-art conditional diffusion models and improved robustness under severe observation corruption.The implementation code is available at: https://github.com/TT-20011031/DynG-Diff

Engineering use of AI forecasting models requires not only high nominal accuracy but also predictable behavior under uncertain inputs. In photovoltaic (PV) forecasting, this requirement is especially challenging because numerical weather prediction (NWP) errors are temporally correlated, state dependent, and physically coupled across variables. Existing evaluations, however, often rely on perfect forecast assumptions or simplistic perturbations that do not reflect these characteristics. This study presents a physically constrained robustness evaluation framework based on simulation, using virtual PV power as a controlled response variable to isolate the propagation of input uncertainty from confounders at the plant level. Six representative machine learning and deep sequence models, including PatchTST, GRU, N-HITS, and LightGBM, are evaluated under dynamic NWP perturbations with heteroscedasticity modulated by clear-sky conditions and Erbs reconstruction that preserves radiation consistency. The results show that sequence models provide stronger noise filtering and temporal resilience than a strong tabular baseline under medium to high disturbance regimes. SHapley Additive exPlanations (SHAP) and Integrated Gradients (IG) further support a feature reallocation tendency at the case level, in which predictive reliance shifts from corrupted future forecasts toward more stable historical observations and deterministic physical priors. A Pareto analysis of accuracy under clean conditions, robustness, and computational latency then translates these findings into engineering implications for robustness assessment and model selection under forecast uncertainty.

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.

Time series forecasting (TSF) underpins consequential decisions in energy, transportation, finance, and healthcare, yet TSF models are almost universally ranked by a single number (e.g., average error) on clean held-out data, under the implicit assumption that it predicts deployed reliability. However, real faults are not i.i.d noise but structured events with temporal shape, broken cross-variable dependencies, regime change coupled with missingness, and causal propagation across a sensing pipeline. Treating TSF robustness as a data-quality problem, we present TS-Fault, a benchmark that evaluates forecasting models under explicit, parameterized fault scenarios with controllable semantic difficulty. TS-Fault organizes recurring failures into four modes along two orthogonal axes (observation- vs mechanism-level; univariate vs multivariate) and injects each fault into the most prediction-critical window via a unified importance score. This design enables robustness to be tested against the structures models actually rely on, rather than reduced to generic noise sensitivity. We evaluate 21 models across 6 datasets, 4 modes, and 5 difficulty levels under a paired clean/corrupt protocol. The results reveal three findings that contradict common leaderboard intuition: (i) clean-data accuracy anti-correlates with robustness; (ii) clean rankings are preserved under observation-level faults but reshuffled under mechanism-level faults; and (iii) all catastrophic failures occur under mechanism-level faults, with foundation models achieving the highest clean-data accuracy yet exhibiting the greatest fragility. The code is publicly available at https://github.com/Ray-zyy/TS-Fault.

We introduce TopoPrimer, a framework that makes the global topological structure of the series population an explicit input to any forecasting model. TopoPrimer improves accuracy across diverse domains, stabilizes forecasts under seasonal demand spikes, and closes the cold-start gap. Precomputed once per domain via persistent homology and spectral sheaf coordinates, TopoPrimer deploys per token for fully-trained models and as a lightweight adapter for pre-trained backbones. Of these two components, sheaf coordinates are the primary accuracy driver. Across four public benchmarks on Chronos and TimesFM, TopoPrimer consistently improves forecasting accuracy, with gains of up to 7.3% MSE on ECL. The topology advantage persists with near-identical magnitude across zero-shot and fine-tuned backbones, suggesting topology and per-series training capture complementary signals. The gains are most pronounced in difficult regimes. Under peak seasonal demand, classical and zero-shot models degrade by up to 50%, while TopoPrimer stays within 10%. At cold start with no item history, TopoPrimer reduces MAE by 27% over a topology-free baseline.

We present TailedTS, a large-scale benchmark dataset derived from Wikipedia hourly page view observations throughout 2024, specifically designed to test time series forecasting models under heavy-tailed, zero-inflated, and non-Gaussian conditions. The dataset comprises approximately 24.69 billion data points spanning roughly 3 million unique Wikipedia pages per month, stored in high-efficiency Apache Parquet format. Wikipedia traffic follows a pronounced power-law distribution where roughly 5% of pages account for over 70% of total page views, creating a natural and rigorous testbed for model robustness against extreme volatility that are absent from or underrepresented in existing benchmarks such as M4, M5, and UCI electricity datasets. TailedTS enables several research tasks. First, we introduce a periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints, revealing that frequently-viewed pages exhibit significantly weaker periodic structure than their less-viewed counterparts, showing direct implications for server allocation and traffic forecasting on large digital platforms. Second, we provide standardized prediction benchmarks evaluated under a suite of non-Gaussian loss functions, including $\ell_1$-norm, Huber, quantile, and $\ell_p$-norm losses, demonstrating that standard Gaussian-based estimators degrade substantially on high-volume page categories, while robust alternatives provide consistent gains across all traffic scales. TailedTS is publicly available at https://doi.org/10.5281/zenodo.17070469.

Accurate forecasting of multivariate time series remains challenging due to the need to capture both short-term fluctuations and long-range temporal dependencies. Transformer-based models have emerged as a powerful approach, but their performance depends critically on the representation of temporal data. Traditional point-wise representations preserve individual time-step information, enabling fine-grained modeling, yet they tend to be computationally expensive and less effective at modeling broader contextual dependencies, limiting their scalability to long sequences. Patch-wise representations aggregate consecutive steps into compact tokens to improve efficiency and model local temporal dynamics, but they often discard fine-grained temporal details that are critical for accurate predictions in volatile or complex time series. We propose IPatch, a multi-resolution Transformer architecture that integrates both point-wise and patch-wise tokens, modeling temporal information at multiple resolutions. Experiments on 7 benchmark datasets demonstrate that IPatch consistently improves forecasting accuracy, robustness to noise, and generalization across various prediction horizons compared to single-representation baselines.

Financial time-series forecasting in real-world high-frequency markets is often hindered by delayed or partially stale observations caused by asynchronous data acquisition and transmission latency. To better reflect such practical conditions, we investigate a simulated delay setting where a portion of historical signals is corrupted by a Zero-Order Hold (ZOH) mechanism, significantly increasing forecasting difficulty through stepwise stagnation artifacts. In this paper, we propose ReLaMix (Residual Latency-Aware Mixing Network), a lightweight extension of TimeMixer that integrates learnable bottleneck compression with residual refinement for robust signal recovery under delayed observations. ReLaMix explicitly suppresses redundancy from repeated stale values while preserving informative market dynamics via residual mixing enhancement. Experiments on a large-scale second-resolution PAXGUSDT benchmark demonstrate that ReLaMix consistently achieves state-of-the-art accuracy across multiple delay ratios and prediction horizons, outperforming strong mixer and Transformer baselines with substantially fewer parameters. Moreover, additional evaluations on BTCUSDT confirm the cross-asset generalization ability of the proposed framework. These results highlight the effectiveness of residual bottleneck mixing for high-frequency financial forecasting under realistic latency-induced staleness.

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 forecasters are widely used across various domains. Among them, MLP (multi-layer perceptron)-based forecasters have been proven to be more robust to noise compared to Transformer-based forecasters. However, MLP struggles to capture complex features, resulting in limitations on capturing long-range dependencies. To address this challenge, we propose XLinear, an MLP-based forecaster for long-range forecasting. Firstly, we decompose the time series into trend and seasonal components. For the trend component which contains long-range characteristics, we design Enhanced Frequency Attention (EFA) to capture long-term dependencies by leveraging frequency-domain operations. Additionally, a CrossFilter Block is proposed for the seasonal component to maintain the model's robustness to noise, avoiding the problems of low robustness often caused by attention mechanisms. Experimental results demonstrate that XLinear achieves state-of-the-art performance on test datasets. While keeping the lightweight architecture and high robustness of MLP-based models, our forecaster outperforms other MLP-based forecasters in capturing long-range dependencies.