ForecastGAN: A Decomposition-Based Adversarial Framework for Multi-Horizon Time Series Forecasting

Time series forecasting is essential across domains from finance to supply chain management. This paper introduces ForecastGAN, a novel decomposition based adversarial framework addressing limitations in existing approaches for multi-horizon predictions. Although transformer models excel in long-term forecasting, they often underperform in short-term scenarios and typically ignore categorical features. ForecastGAN operates through three integrated modules: a Decomposition Module that extracts seasonality and trend components; a Model Selection Module that identifies optimal neural network configurations based on forecasting horizon; and an Adversarial Training Module that enhances prediction robustness through Conditional Generative Adversarial Network training. Unlike conventional approaches, ForecastGAN effectively integrates both numerical and categorical features. We validate our framework on eleven benchmark multivariate time series datasets that span various forecasting horizons. The results show that ForecastGAN consistently outperforms state-of-the-art transformer models for short-term forecasting while remaining competitive for long-term horizons. This research establishes a more generalizable approach to time series forecasting that adapts to specific contexts while maintaining strong performance across diverse data characteristics without extensive hyperparameter tuning.

HTMformer: Hybrid Time and Multivariate Transformer for Time Series Forecasting

Transformer-based methods have achieved impressive results in time series forecasting. However, existing Transformers still exhibit limitations in sequence modeling as they tend to overemphasize temporal dependencies. This incurs additional computational overhead without yielding corresponding performance gains. We find that the performance of Transformers is highly dependent on the embedding method used to learn effective representations. To address this issue, we extract multivariate features to augment the effective information captured in the embedding layer, yielding multidimensional embeddings that convey richer and more meaningful sequence representations. These representations enable Transformer-based forecasters to better understand the series. Specifically, we introduce Hybrid Temporal and Multivariate Embeddings (HTME). The HTME extractor integrates a lightweight temporal feature extraction module with a carefully designed multivariate feature extraction module to provide complementary features, thereby achieving a balance between model complexity and performance. By combining HTME with the Transformer architecture, we present HTMformer, leveraging the enhanced feature extraction capability of the HTME extractor to build a lightweight forecaster. Experiments conducted on eight real-world datasets demonstrate that our approach outperforms existing baselines in both accuracy and efficiency.

Benchmarking M-LTSF: Frequency and Noise-Based Evaluation of Multivariate Long Time Series Forecasting Models

Understanding the robustness of deep learning models for multivariate long-term time series forecasting (M-LTSF) remains challenging, as evaluations typically rely on real-world datasets with unknown noise properties. We propose a simulation-based evaluation framework that generates parameterizable synthetic datasets, where each dataset instance corresponds to a different configuration of signal components, noise types, signal-to-noise ratios, and frequency characteristics. These configurable components aim to model real-world multivariate time series data without the ambiguity of unknown noise. This framework enables fine-grained, systematic evaluation of M-LTSF models under controlled and diverse scenarios. We benchmark four representative architectures S-Mamba (state-space), iTransformer (transformer-based), R-Linear (linear), and Autoformer (decomposition-based). Our analysis reveals that all models degrade severely when lookback windows cannot capture complete periods of seasonal patters in the data. S-Mamba and Autoformer perform best on sawtooth patterns, while R-Linear and iTransformer favor sinusoidal signals. White and Brownian noise universally degrade performance with lower signal-to-noise ratio while S-Mamba shows specific trend-noise and iTransformer shows seasonal-noise vulnerability. Further spectral analysis shows that S-Mamba and iTransformer achieve superior frequency reconstruction. This controlled approach, based on our synthetic and principle-driven testbed, offers deeper insights into model-specific strengths and limitations through the aggregation of MSE scores and provides concrete guidance for model selection based on signal characteristics and noise conditions.

CoRA: Covariate-Aware Adaptation of Time Series Foundation Models

Time Series Foundation Models (TSFMs) have shown significant impact through their model capacity, scalability, and zero-shot generalization. However, due to the heterogeneity of inter-variate dependencies and the backbone scalability on large-scale multivariate datasets, most TSFMs are typically pre-trained on univariate time series. This limitation renders them oblivious to crucial information from diverse covariates in real-world forecasting tasks. To further enhance the performance of TSFMs, we propose a general covariate-aware adaptation (CoRA) framework for TSFMs. It leverages pre-trained backbones of foundation models while effectively incorporating exogenous covariates from various modalities, including time series, language, and images, to improve the quality of predictions. Technically, CoRA maintains the equivalence of initialization and parameter consistency during adaptation. With preserved backbones of foundation models as frozen feature extractors, the outcome embeddings from foundation models are empirically demonstrated more informative than raw data. Further, CoRA employs a novel Granger Causality Embedding (GCE) to automatically evaluate covariates regarding their causal predictability with respect to the target variate. We incorporate these weighted embeddings with a zero-initialized condition-injection mechanism, avoiding catastrophic forgetting of pre-trained foundation models and gradually integrates exogenous information. Extensive experiments show that CoRA of TSFMs surpasses state-of-the-art covariate-aware deep forecasters with full or few-shot training samples, achieving 31.1% MSE reduction on covariate-aware forecasting. Compared to other adaptation methods, CoRA exhibits strong compatibility with various advanced TSFMs and extends the scope of covariates to other modalities, presenting a practical paradigm for the application of TSFMs.

STaTS: Structure-Aware Temporal Sequence Summarization via Statistical Window Merging

Time series data often contain latent temporal structure, transitions between locally stationary regimes, repeated motifs, and bursts of variability, that are rarely leveraged in standard representation learning pipelines. Existing models typically operate on raw or fixed-window sequences, treating all time steps as equally informative, which leads to inefficiencies, poor robustness, and limited scalability in long or noisy sequences. We propose STaTS, a lightweight, unsupervised framework for Structure-Aware Temporal Summarization that adaptively compresses both univariate and multivariate time series into compact, information-preserving token sequences. STaTS detects change points across multiple temporal resolutions using a BIC-based statistical divergence criterion, then summarizes each segment using simple functions like the mean or generative models such as GMMs. This process achieves up to 30x sequence compression while retaining core temporal dynamics. STaTS operates as a model-agnostic preprocessor and can be integrated with existing unsupervised time series encoders without retraining. Extensive experiments on 150+ datasets, including classification tasks on the UCR-85, UCR-128, and UEA-30 archives, and forecasting on ETTh1 and ETTh2, ETTm1, and Electricity, demonstrate that STaTS enables 85-90\% of the full-model performance while offering dramatic reductions in computational cost. Moreover, STaTS improves robustness under noise and preserves discriminative structure, outperforming uniform and clustering-based compression baselines. These results position STaTS as a principled, general-purpose solution for efficient, structure-aware time series modeling.

From News to Returns: A Granger-Causal Hypergraph Transformer on the Sphere

We propose the Causal Sphere Hypergraph Transformer (CSHT), a novel architecture for interpretable financial time-series forecasting that unifies \emph{Granger-causal hypergraph structure}, \emph{Riemannian geometry}, and \emph{causally masked Transformer attention}. CSHT models the directional influence of financial news and sentiment on asset returns by extracting multivariate Granger-causal dependencies, which are encoded as directional hyperedges on the surface of a hypersphere. Attention is constrained via angular masks that preserve both temporal directionality and geometric consistency. Evaluated on S\&P 500 data from 2018 to 2023, including the 2020 COVID-19 shock, CSHT consistently outperforms baselines across return prediction, regime classification, and top-asset ranking tasks. By enforcing predictive causal structure and embedding variables in a Riemannian manifold, CSHT delivers both \emph{robust generalisation across market regimes} and \emph{transparent attribution pathways} from macroeconomic events to stock-level responses. These results suggest that CSHT is a principled and practical solution for trustworthy financial forecasting under uncertainty.

DPANet: Dual Pyramid Attention Network for Multivariate Time Series Forecasting

We conducted rigorous ablation studies to validate DPANet's key components (Table \ref{tab:ablation-study}). The full model consistently outperforms all variants. To test our dual-domain hypothesis, we designed two specialized versions: a Temporal-Only model (fusing two identical temporal pyramids) and a Frequency-Only model (fusing two spectral pyramids). Both variants underperformed significantly, confirming that the fusion of heterogeneous temporal and frequency information is critical. Furthermore, replacing the cross-attention mechanism with a simpler method (w/o Cross-Fusion) caused the most severe performance degradation. This result underscores that our interactive fusion block is the most essential component.

IBN: An Interpretable Bidirectional-Modeling Network for Multivariate Time Series Forecasting with Variable Missing

Multivariate time series forecasting (MTSF) often faces challenges from missing variables, which hinder conventional spatial-temporal graph neural networks in modeling inter-variable correlations. While GinAR addresses variable missing using attention-based imputation and adaptive graph learning for the first time, it lacks interpretability and fails to capture more latent temporal patterns due to its simple recursive units (RUs). To overcome these limitations, we propose the Interpretable Bidirectional-modeling Network (IBN), integrating Uncertainty-Aware Interpolation (UAI) and Gaussian kernel-based Graph Convolution (GGCN). IBN estimates the uncertainty of reconstructed values using MC Dropout and applies an uncertainty-weighted strategy to mitigate high-risk reconstructions. GGCN explicitly models spatial correlations among variables, while a bidirectional RU enhances temporal dependency modeling. Extensive experiments show that IBN achieves state-of-the-art forecasting performance under various missing-rate scenarios, providing a more reliable and interpretable framework for MTSF with missing variables. Code is available at: https://github.com/zhangth1211/NICLab-IBN.

Diffusion-Based Scenario Tree Generation for Multivariate Time Series Prediction and Multistage Stochastic Optimization

Stochastic forecasting is critical for efficient decision-making in uncertain systems, such as energy markets and finance, where estimating the full distribution of future scenarios is essential. We propose Diffusion Scenario Tree (DST), a general framework for constructing scenario trees for multivariate prediction tasks using diffusion-based probabilistic forecasting models. DST recursively samples future trajectories and organizes them into a tree via clustering, ensuring non-anticipativity (decisions depending only on observed history) at each stage. We evaluate the framework on the optimization task of energy arbitrage in New York State's day-ahead electricity market. Experimental results show that our approach consistently outperforms the same optimization algorithms that use scenario trees from more conventional models and Model-Free Reinforcement Learning baselines. Furthermore, using DST for stochastic optimization yields more efficient decision policies, achieving higher performance by better handling uncertainty than deterministic and stochastic MPC variants using the same diffusion-based forecaster.

From Patterns to Predictions: A Shapelet-Based Framework for Directional Forecasting in Noisy Financial Markets

Directional forecasting in financial markets requires both accuracy and interpretability. Before the advent of deep learning, interpretable approaches based on human-defined patterns were prevalent, but their structural vagueness and scale ambiguity hindered generalization. In contrast, deep learning models can effectively capture complex dynamics, yet often offer limited transparency. To bridge this gap, we propose a two-stage framework that integrates unsupervised pattern extracion with interpretable forecasting. (i) SIMPC segments and clusters multivariate time series, extracting recurrent patterns that are invariant to amplitude scaling and temporal distortion, even under varying window sizes. (ii) JISC-Net is a shapelet-based classifier that uses the initial part of extracted patterns as input and forecasts subsequent partial sequences for short-term directional movement. Experiments on Bitcoin and three S&P 500 equities demonstrate that our method ranks first or second in 11 out of 12 metric--dataset combinations, consistently outperforming baselines. Unlike conventional deep learning models that output buy-or-sell signals without interpretable justification, our approach enables transparent decision-making by revealing the underlying pattern structures that drive predictive outcomes.