Long-Term Time Series Forecasting

Time series forecasting plays a pivotal role in critical sectors such as finance, energy, transportation, and meteorology. However, Long-term Time Series Forecasting (LTSF) remains a significant challenge because real-world signals contain highly entangled temporal dynamics that are difficult to fully capture from a purely 1D perspective. To break this representation bottleneck, we propose TriTS, a novel cross-modal disentanglement framework that projects 1D time series into orthogonal time, frequency, and 2D-vision spaces.To seamlessly bridge the 1D-to-2D modality gap without the prohibitive $O(N^2)$ computational overhead of Vision Transformers (ViTs), we introduce a Period-Aware Reshaping strategy and incorporate Visual Mamba (Vim). This approach efficiently models cross-period dependencies as global visual textures while maintaining linear computational complexity. Complementing this, we design a Multi-Resolution Wavelet Mixing (MR-WM) module for the frequency modality, which explicitly decouples non-stationary signals into trend and noise components to achieve fine-grained time-frequency localization. Finally, a streaming linear branch is retained in the time domain to anchor numerical stability. By dynamically fusing these three complementary representations, TriTS effectively adapts to diverse data contexts. Extensive experiments across multiple benchmark datasets demonstrate that TriTS achieves state-of-the-art (SOTA) performance, fundamentally outperforming existing vision-based forecasters by drastically reducing both parameter count and inference latency.

Augmentation has become a central technique for improving deep forecasting models, but classification-style transformations tend to break the coherence between the look-back window and its continuous future target. We describe a simple procedure that unfolds the joint input-target sequence into overlapping sliding windows, randomly reorders a controlled fraction of them-prioritized by a lightweight variance criterion-and reconstructs the sequence by averaging across the overlaps, producing synthetic samples with controlled variation while limiting temporal distortion. The procedure is model-agnostic, introduces only three interpretable hyperparameters, and achieves strong improvements over a comprehensive set of competing augmentations across nine long-term forecasting benchmarks with five backbone families (TSMixer, DLinear, PatchTST, TiDE, LightTS) and four short-term traffic benchmarks with PatchTST. Component-wise ablations, hyperparameter sensitivity studies, distributional-alignment diagnostics, probabilistic forecasting evaluation, and a transfer experiment to univariate and multivariate time series classification clarify the contribution of each design choice.

Multivariate time series forecasting is fundamental to numerous domains such as energy, finance, and environmental monitoring, where complex temporal dependencies and cross-variable interactions pose enduring challenges. Existing Transformer-based methods capture temporal correlations through attention mechanisms but suffer from quadratic computational cost, while state-space models like Mamba achieve efficient long-context modeling yet lack explicit temporal pattern recognition. Therefore we introduce UniMamba, a unified spatial-temporal forecasting framework that integrates efficient state-space dynamics with attention-based dependency learning. UniMamba employs a Mamba Variate-Channel Encoding Layer enhanced with FFT-Laplace Transform and TCN to capture global temporal dependencies, and a Spatial Temporal Attention Layer to jointly model inter-variate correlations and temporal evolution. A Feedforward Temporal Dynamics Layer further fuses continuous and discrete contexts for accurate forecasting. Comprehensive experiments on eight public benchmark datasets demonstrate that UniMamba consistently outperforms state-of-the-art forecasting models in both forecasting accuracy and computational efficiency, establishing a scalable and robust solution for long-sequence multivariate time-series prediction.

Modeling multiscale patterns is crucial for long-term time series forecasting (TSF). However, redundancy and noise in time series, together with semantic gaps between non-adjacent scales, make the efficient alignment and integration of multi-scale temporal dependencies challenging. To address this, we propose SEMixer, a lightweight multiscale model designed for long-term TSF. SEMixer features two key components: a Random Attention Mechanism (RAM) and a Multiscale Progressive Mixing Chain (MPMC). RAM captures diverse time-patch interactions during training and aggregates them via dropout ensemble at inference, enhancing patch-level semantics and enabling MLP-Mixer to better model multi-scale dependencies. MPMC further stacks RAM and MLP-Mixer in a memory-efficient manner, achieving more effective temporal mixing. It addresses semantic gaps across scales and facilitates better multiscale modeling and forecasting performance. We not only validate the effectiveness of SEMixer on 10 public datasets, but also on the \textit{2025 CCF AlOps Challenge} based on 21GB real wireless network data, where SEMixer achieves third place. The code is available at the link https://github.com/Meteor-Stars/SEMixer.

When training autoregressive models to forecast dynamical systems, a critical question arises: how far into the future should the model be trained to predict for optimal performance? In this work, we address this question by analyzing the relationship between the geometry of the loss landscape and the training time horizon. Using dynamical systems theory, we prove that loss minima for long horizons generalize well to short-term forecasts, whereas minima found on short horizons result in worse long-term predictions. However, we also prove that the loss landscape becomes rougher as the training horizon grows, making long-horizon training inherently challenging. We validate our theory through numerical experiments and discuss practical implications for selecting training horizons. Our results provide a principled foundation for hyperparameter optimization in autoregressive forecasting models.

Training time-series forecasting models poses unique challenges in loss function design. Most existing approaches adopt temporal mean squared error, but this study reveals two critical limitations: (1) it ignores the presence of label autocorrelation, which biases it from the true label sequence likelihood; (2) it involves excessive number of tasks, which complicates optimization, especially for long-term forecasting. To address these issues, we introduce Time-o1, a transform-enhanced loss function for time-series forecasting. The central idea is to transform the label sequence into decorrelated components with discriminated significance. Models are then trained to align the most significant components, thereby effectively mitigating label autocorrelation and reducing task amount. Experiments demonstrate that Time-o1 achieves state-of-the-art performance and is compatible with various forecast models. Code is available at https://github.com/Master-PLC/Time-o1.

Teleoperation systems must be aware of the human's workload during missions to maintain operator performance. Prior work employed wearable physiological sensor response metrics to estimate current human workload; however, these estimates only enable robots to respond to under- or overload conditions reactively. Current human workload prediction approaches are limited to very short prediction horizons and fail to investigate variable lag horizons' impact on those predictions. This manuscript investigates physiological sensor driven human workload prediction focusing on the impact of lag horizons on both univariate and multivariate time series forecasting models, with longer prediction horizons than the workload prediction state-of-the-art (i.e., > 30 seconds using Long Short-Term Memory networks). Models were trained using data from a 64 participant non-sedentary supervisory environment NASA Multi-Attribute Task Battery-II human subjects evaluation. A key finding is that univariate workload predictions required 240 second lag horizons, whereas multivariate workload predictions sufficed with 120 second lag horizons. This finding indicates additional workload components reduce lag horizon requirements, enabling more efficient models with longer prediction horizons.

Traffic forecasting uses recent measurements by sensors installed at chosen locations to forecast the future road traffic. Existing work either assumes all locations are equipped with sensors or focuses on short-term forecast. This paper studies partial sensing forecast of long-term traffic, assuming sensors are available only at some locations. The problem is challenging due to the unknown data distribution at unsensed locations, the intricate spatio-temporal correlation in long-term forecasting, as well as noise to traffic patterns. We propose a Spatio-temporal Long-term Partial sensing Forecast model (SLPF) for traffic prediction, with several novel contributions, including a rank-based embedding technique to reduce the impact of noise in data, a spatial transfer matrix to overcome the spatial distribution shift from sensed locations to unsensed locations, and a multi-step training process that utilizes all available data to successively refine the model parameters for better accuracy. Extensive experiments on several real-world traffic datasets demonstrate its superior performance. Our source code is at https://github.com/zbliu98/SLPF