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.

Recent studies have shown that deep learning models such as RNNs and Transformers have brought significant performance gains for long-term forecasting of time series because they effectively utilize historical information. We found, however, that there is still great room for improvement in how to preserve historical information in neural networks while avoiding overfitting to noise present in the history. Addressing this allows better utilization of the capabilities of deep learning models. To this end, we design a Frequency improved Legendre Memory model, or FiLM: it applies Legendre polynomial projections to approximate historical information, uses Fourier projection to remove noise, and adds a low-rank approximation to speed up computation. Our empirical studies show that the proposed FiLM significantly improves the accuracy of state-of-the-art models in multivariate and univariate long-term forecasting by (19.2%, 22.6%), respectively. We also demonstrate that the representation module developed in this work can be used as a general plugin to improve the long-term prediction performance of other deep learning modules.

Time series forecasting in real world environments faces significant challenges non stationarity, multi scale temporal patterns, and distributional shifts that degrade model stability and accuracy. This study propose AdaMamba, a unified forecasting architecture that integrates adaptive normalization, multi scale trend extraction, and contextual sequence modeling to address these challenges. AdaMamba begins with an Adaptive Normalization Block that removes non stationary components through multi scale convolutional trend extraction and channel wise recalibration, enabling consistent detrending and variance stabilization. The normalized sequence is then processed by a Context Encoder that combines patch wise embeddings, positional encoding, and a Mamba enhanced Transformer layer with a mixture of experts feed forward module, allowing efficient modeling of both long range dependencies and local temporal dynamics. A lightweight prediction head generates multi horizon forecasts, and a denormalization mechanism reconstructs outputs by reintegrating local trends to ensure robustness under varying temporal conditions. AdaMamba provides strong representational capacity with modular extensibility, supporting deterministic prediction and compatibility with probabilistic extensions. Its design effectively mitigates covariate shift and enhances predictive reliability across heterogeneous datasets. Experimental evaluations demonstrate that AdaMamba's combination of adaptive normalization and expert augmented contextual modeling yields consistent improvements in stability and accuracy over conventional Transformer based baselines.

This paper presents Naga, a deep State Space Model (SSM) encoding approach inspired by structural concepts from Vedic mathematics. The proposed method introduces a bidirectional representation for time series by jointly processing forward and time-reversed input sequences. These representations are then combined through an element-wise (Hadamard) interaction, resulting in a Vedic-inspired encoding that enhances the model's ability to capture temporal dependencies across distant time steps. We evaluate Naga on multiple long-term time series forecasting (LTSF) benchmarks, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, Traffic, and ILI. The experimental results show that Naga outperforms 28 current state of the art models and demonstrates improved efficiency compared to existing deep SSM-based approaches. The findings suggest that incorporating structured, Vedic-inspired decomposition can provide an interpretable and computationally efficient alternative for long-range sequence modeling.

Long-term time series forecasting (LTSF) represents a critical frontier in time series analysis, characterized by extensive input sequences, as opposed to the shorter spans typical of traditional approaches. While longer sequences inherently offer richer information for enhanced predictive precision, prevailing studies often respond by escalating model complexity. These intricate models can inflate into millions of parameters, resulting in prohibitive parameter scales. Our study demonstrates, through both theoretical and empirical evidence, that decomposition is key to containing excessive model inflation while achieving uniformly superior and robust results across various datasets. Remarkably, by tailoring decomposition to the intrinsic dynamics of time series data, our proposed model outperforms existing benchmarks, using over 99\% fewer parameters than the majority of competing methods.

In long-term time series forecasting (LTSF) tasks, an increasing number of works have acknowledged that discrete time series originate from continuous dynamic systems and have attempted to model their underlying dynamics. Recognizing the chaotic nature of real-world data, our model, Attraos, incorporates chaos theory into LTSF, perceiving real-world time series as low-dimensional observations from unknown high-dimensional chaotic dynamical systems. Under the concept of attractor invariance, Attraos utilizes non-parametric Phase Space Reconstruction embedding along with a novel multi-resolution dynamic memory unit to memorize historical dynamical structures, and evolves by a frequency-enhanced local evolution strategy. Detailed theoretical analysis and abundant empirical evidence consistently show that Attraos outperforms various LTSF methods on mainstream LTSF datasets and chaotic datasets with only one-twelfth of the parameters compared to PatchTST.

The interaction between Fourier transform and deep learning opens new avenues for long-term time series forecasting (LTSF). We propose a new perspective to reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency components can be viewed as the coefficients of cosine and sine basis functions at tiered frequency levels, respectively. We argue existing Fourier-based methods do not involve basis functions thus fail to interpret frequency coefficients precisely and consider the time-frequency relationship sufficiently, leading to inconsistent starting cycles and inconsistent series length issues. Differing from existing approaches, FBM (i) embeds the discrete Fourier transform with basis functions, and then (ii) can enable plug-and-play in various types of neural networks for better performance. FBM extracts explicit frequency features while preserving temporal characteristics, enabling the mapping network to capture the time-frequency relationships.

Recent deep learning models for Long-term Time Series Forecasting (LTSF) often emphasize complex, handcrafted designs, while simpler architectures like linear models or MLPs have often outperformed these intricate solutions. In this paper, we revisit and organize the core ideas behind several key techniques, such as redundancy reduction and multi-scale modeling, which are frequently employed in advanced LTSF models. Our goal is to streamline these ideas for more efficient deep learning utilization. To this end, we introduce TimeCapsule, a model built around the principle of high-dimensional information compression that unifies these techniques in a generalized yet simplified framework. Specifically, we model time series as a 3D tensor, incorporating temporal, variate, and level dimensions, and leverage mode production to capture multi-mode dependencies while achieving dimensionality compression. We propose an internal forecast within the compressed representation domain, supported by the Joint-Embedding Predictive Architecture (JEPA), to monitor the learning of predictive representations. Extensive experiments on challenging benchmarks demonstrate the versatility of our method, showing that TimeCapsule can achieve state-of-the-art performance.

Long-term time series forecasting is critical in domains such as finance, economics, and energy, where accurate and reliable predictions over extended horizons drive strategic decision-making. Despite the progress in machine learning-based models, the impact of temporal noise in extended lookback windows remains underexplored, often degrading model performance and computational efficiency. In this paper, we propose a novel framework that addresses these challenges by integrating the Discrete Wavelet Transform (DWT) and Discrete Cosine Transform (DCT) to perform noise reduction and extract robust long-term features. These transformations enable the separation of meaningful temporal patterns from noise in both the time and frequency domains. To complement this, we introduce a lightweight low-rank linear prediction layer that not only reduces the influence of residual noise but also improves memory efficiency. Our approach demonstrates competitive robustness to noisy input, significantly reduces computational complexity, and achieves competitive or state-of-the-art forecasting performance across diverse benchmark datasets. Extensive experiments reveal that the proposed framework is particularly effective in scenarios with high noise levels or irregular patterns, making it well suited for real-world forecasting tasks. The code is available in https://github.com/forgee-master/HADL.

Long-term time series forecasting (LTSF) involves predicting a large number of future values of a time series based on the past values and is an essential task in a wide range of domains including weather forecasting, stock market analysis, disease outbreak prediction. Over the decades LTSF algorithms have transitioned from statistical models to deep learning models like transformer models. Despite the complex architecture of transformer based LTSF models `Are Transformers Effective for Time Series Forecasting? (Zeng et al., 2023)' showed that simple linear models can outperform the state-of-the-art transformer based LTSF models. Recently, quantum machine learning (QML) is evolving as a domain to enhance the capabilities of classical machine learning models. In this paper we initiate the application of QML to LTSF problems by proposing QuLTSF, a simple hybrid QML model for multivariate LTSF. Through extensive experiments on a widely used weather dataset we show the advantages of QuLTSF over the state-of-the-art classical linear models, in terms of reduced mean squared error and mean absolute error.