Recent Transformer- and MLP-based models have demonstrated strong performance in long-term time series forecasting, yet Transformers remain limited by their quadratic complexity and permutation-equivariant attention, while MLPs exhibit spectral bias. We propose HaKAN, a versatile model based on Kolmogorov-Arnold Networks (KANs), leveraging Hahn polynomial-based learnable activation functions and providing a lightweight and interpretable alternative for multivariate time series forecasting. Our model integrates channel independence, patching, a stack of Hahn-KAN blocks with residual connections, and a bottleneck structure comprised of two fully connected layers. The Hahn-KAN block consists of inter- and intra-patch KAN layers to effectively capture both global and local temporal patterns. Extensive experiments on various forecasting benchmarks demonstrate that our model consistently outperforms recent state-of-the-art methods, with ablation studies validating the effectiveness of its core components.

Multivariate time series forecasting is of central importance in modern intelligent decision systems. The dynamics of multivariate time series are jointly characterized by temporal dependencies and spatial correlations. Hence, it is equally important to build the forecasting models from both perspectives. The real-world multivariate time series data often presents spatial correlations that show structures and evolve dynamically. To capture such dynamic spatial structures, the existing forecasting approaches often rely on a two-stage learning process (learning dynamic series representations and then generating spatial structures), which is sensitive to the small time-window input data and has high variance. To address this, we propose a novel forecasting model with a structured matrix basis. At its core is a dynamic spatial structure generation function whose output space is well-constrained and the generated structures have lower variance, meanwhile, it is more expressive and can offer interpretable dynamics. This is achieved via a novel structured parameterization and imposing structure regularization on the matrix basis. The resulting forecasting model can achieve up to $8.5\%$ improvements over the existing methods on six benchmark datasets, and meanwhile, it enables us to gain insights into the dynamics of underlying systems.

Traditional Transformers face a major bottleneck in long-sequence time series forecasting due to their quadratic complexity $(\mathcal{O}(T^2))$ and their limited ability to effectively exploit frequency-domain information. Inspired by RWKV's $\mathcal{O}(T)$ linear attention and frequency-domain modeling, we propose FRWKV, a frequency-domain linear-attention framework that overcomes these limitations. Our model integrates linear attention mechanisms with frequency-domain analysis, achieving $\mathcal{O}(T)$ computational complexity in the attention path while exploiting spectral information to enhance temporal feature representations for scalable long-sequence modeling. Across eight real-world datasets, FRWKV achieves a first-place average rank. Our ablation studies confirm the critical roles of both the linear attention and frequency-encoder components. This work demonstrates the powerful synergy between linear attention and frequency analysis, establishing a new paradigm for scalable time series modeling. Code is available at this repository: https://github.com/yangqingyuan-byte/FRWKV.

Accurate forecasting of multivariate time series data remains a formidable challenge, particularly due to the growing complexity of temporal dependencies in real-world scenarios. While neural network-based models have achieved notable success in this domain, complex channel-dependent models often suffer from performance degradation compared to channel-independent models that do not consider the relationship between components but provide high robustness due to small capacity. In this work, we propose HN-MVTS, a novel architecture that integrates a hypernetwork-based generative prior with an arbitrary neural network forecasting model. The input of this hypernetwork is a learnable embedding matrix of time series components. To restrict the number of new parameters, the hypernetwork learns to generate the weights of the last layer of the target forecasting networks, serving as a data-adaptive regularizer that improves generalization and long-range predictive accuracy. The hypernetwork is used only during the training, so it does not increase the inference time compared to the base forecasting model. Extensive experiments on eight benchmark datasets demonstrate that application of HN-MVTS to the state-of-the-art models (DLinear, PatchTST, TSMixer, etc.) typically improves their performance. Our findings suggest that hypernetwork-driven parameterization offers a promising direction for enhancing existing forecasting techniques in complex scenarios.

Irregular multivariate time series (IMTS), characterized by uneven sampling and inter-variate asynchrony, fuel many forecasting applications yet remain challenging to model efficiently. Canonical Pre-Alignment (CPA) has been widely adopted in IMTS modeling by padding zeros at every global timestamp, thereby alleviating inter-variate asynchrony and unifying the series length, but its dense zero-padding inflates the pre-aligned series length, especially when numerous variates are present, causing prohibitive compute overhead. Recent graph-based models with patching strategies sidestep CPA, but their local message passing struggles to capture global inter-variate correlations. Therefore, we posit that CPA should be retained, with the pre-aligned series properly handled by the model, enabling it to outperform state-of-the-art graph-based baselines that sidestep CPA. Technically, we propose KAFNet, a compact architecture grounded in CPA for IMTS forecasting that couples (1) Pre-Convolution module for sequence smoothing and sparsity mitigation, (2) Temporal Kernel Aggregation module for learnable compression and modeling of intra-series irregularity, and (3) Frequency Linear Attention blocks for the low-cost inter-series correlations modeling in the frequency domain. Experiments on multiple IMTS datasets show that KAFNet achieves state-of-the-art forecasting performance, with a 7.2$\times$ parameter reduction and a 8.4$\times$ training-inference acceleration.

In multivariate time series forecasting (MTSF), accurately modeling the intricate dependencies among multiple variables remains a significant challenge due to the inherent limitations of traditional approaches. Most existing models adopt either \textbf{channel-independent} (CI) or \textbf{channel-dependent} (CD) strategies, each presenting distinct drawbacks. CI methods fail to leverage the potential insights from inter-channel interactions, resulting in models that may not fully exploit the underlying statistical dependencies present in the data. Conversely, CD approaches often incorporate too much extraneous information, risking model overfitting and predictive inefficiency. To address these issues, we introduce the Adaptive Forecasting Transformer (\textbf{Adapformer}), an advanced Transformer-based framework that merges the benefits of CI and CD methodologies through effective channel management. The core of Adapformer lies in its dual-stage encoder-decoder architecture, which includes the \textbf{A}daptive \textbf{C}hannel \textbf{E}nhancer (\textbf{ACE}) for enriching embedding processes and the \textbf{A}daptive \textbf{C}hannel \textbf{F}orecaster (\textbf{ACF}) for refining the predictions. ACE enhances token representations by selectively incorporating essential dependencies, while ACF streamlines the decoding process by focusing on the most relevant covariates, substantially reducing noise and redundancy. Our rigorous testing on diverse datasets shows that Adapformer achieves superior performance over existing models, enhancing both predictive accuracy and computational efficiency, thus making it state-of-the-art in MTSF.

The forecasting of irregular multivariate time series (IMTS) is crucial in key areas such as healthcare, biomechanics, climate science, and astronomy. However, achieving accurate and practical predictions is challenging due to two main factors. First, the inherent irregularity and data missingness in irregular time series make modeling difficult. Second, most existing methods are typically complex and resource-intensive. In this study, we propose a general framework called APN to address these challenges. Specifically, we design a novel Time-Aware Patch Aggregation (TAPA) module that achieves adaptive patching. By learning dynamically adjustable patch boundaries and a time-aware weighted averaging strategy, TAPA transforms the original irregular sequences into high-quality, regularized representations in a channel-independent manner. Additionally, we use a simple query module to effectively integrate historical information while maintaining the model's efficiency. Finally, predictions are made by a shallow MLP. Experimental results on multiple real-world datasets show that APN outperforms existing state-of-the-art methods in both efficiency and accuracy.

Multivariate time series forecasting (MTSF) plays a vital role in a wide range of real-world applications, such as weather prediction and traffic flow forecasting. Although recent advances have significantly improved the modeling of temporal dynamics and inter-variable dependencies, most existing methods overlook index-related descriptive information, such as timestamps and variable indices, which carry rich contextual semantics. To unlock the potential of such information and take advantage of the lightweight and powerful periodic capture ability of MLP-based architectures, we propose IndexNet, an MLP-based framework augmented with an Index Embedding (IE) module. The IE module consists of two key components: Timestamp Embedding (TE) and Channel Embedding (CE). Specifically, TE transforms timestamps into embedding vectors and injects them into the input sequence, thereby improving the model's ability to capture long-term complex periodic patterns. In parallel, CE assigns each variable a unique and trainable identity embedding based on its index, allowing the model to explicitly distinguish between heterogeneous variables and avoid homogenized predictions when input sequences seem close. Extensive experiments on 12 diverse real-world datasets demonstrate that IndexNet achieves comparable performance across mainstream baselines, validating the effectiveness of our temporally and variably aware design. Moreover, plug-and-play experiments and visualization analyses further reveal that IndexNet exhibits strong generality and interpretability, two aspects that remain underexplored in current MTSF research.

Missing values are common in real-world time series, and multivariate time series forecasting with missing values (MTSF-M) has become a crucial area of research for ensuring reliable predictions. To address the challenge of missing data, current approaches have developed an imputation-then-prediction framework that uses imputation modules to fill in missing values, followed by forecasting on the imputed data. However, this framework overlooks a critical issue: there is no ground truth for the missing values, making the imputation process susceptible to errors that can degrade prediction accuracy. In this paper, we conduct a systematic empirical study and reveal that imputation without direct supervision can corrupt the underlying data distribution and actively degrade prediction accuracy. To address this, we propose a paradigm shift that moves away from imputation and directly predicts from the partially observed time series. We introduce Consistency-Regularized Information Bottleneck (CRIB), a novel framework built on the Information Bottleneck principle. CRIB combines a unified-variate attention mechanism with a consistency regularization scheme to learn robust representations that filter out noise introduced by missing values while preserving essential predictive signals. Comprehensive experiments on four real-world datasets demonstrate the effectiveness of CRIB, which predicts accurately even under high missing rates. Our code implementation is available in https://github.com/Muyiiiii/CRIB. However, due to uncontrollable factors such as data collection difficulties and transmission failures (Li et al., 2023; Marisca et al., 2022; Cini et al., 2021; Zhang et al., 2025a), real-world multivariate time series data is often partially observed, with missing values scattered throughout the series.

In this paper, we propose a novel Spatial Balance Attention block for spatiotemporal forecasting. To strike a balance between obeying spatial proximity and capturing global correlation, we partition the spatial graph into a set of subgraphs and instantiate Intra-subgraph Attention to learn local spatial correlation within each subgraph; to capture the global spatial correlation, we further aggregate the nodes to produce subgraph representations and achieve message passing among the subgraphs via Inter-subgraph Attention. Building on the proposed Spatial Balance Attention block, we develop a multiscale spatiotemporal forecasting model by progressively increasing the subgraph scales. The resulting model is both scalable and able to produce structured spatial correlation, and meanwhile, it is easy to implement. We evaluate its efficacy and efficiency against the existing models on real-world spatiotemporal datasets from medium to large sizes. The experimental results show that it can achieve performance improvements up to 7.7% over the baseline methods at low running costs.