Transformer-based and MLP-based methods have emerged as leading approaches in time series forecasting (TSF). However, real-world time series often show different patterns at different scales, and future changes are shaped by the interplay of these overlapping scales, requiring high-capacity models. While Transformer-based methods excel in capturing long-range dependencies, they suffer from high computational complexities and tend to overfit. Conversely, MLP-based methods offer computational efficiency and adeptness in modeling temporal dynamics, but they struggle with capturing temporal patterns with complex scales effectively. Based on the observation of multi-scale entanglement effect in time series, we propose a novel MLP-based Adaptive Multi-Scale Decomposition (AMD) framework for TSF. Our framework decomposes time series into distinct temporal patterns at multiple scales, leveraging the Multi-Scale Decomposable Mixing (MDM) block to dissect and aggregate these patterns. Complemented by the Dual Dependency Interaction (DDI) block and the Adaptive Multi-predictor Synthesis (AMS) block, our approach effectively models both temporal and channel dependencies and utilizes autocorrelation to refine multi-scale data integration. Comprehensive experiments demonstrate our AMD framework not only overcomes the limitations of existing methods but also consistently achieves state-of-the-art performance across various datasets.

Time series forecasting methods generally fall into two main categories: Channel Independent (CI) and Channel Dependent (CD) strategies. While CI overlooks important covariate relationships, CD captures all dependencies without distinction, introducing noise and reducing generalization. Recent advances in Channel Clustering (CC) aim to refine dependency modeling by grouping channels with similar characteristics and applying tailored modeling techniques. However, coarse-grained clustering struggles to capture complex, time-varying interactions effectively. To address these challenges, we propose TimeFilter, a GNN-based framework for adaptive and fine-grained dependency modeling. After constructing the graph from the input sequence, TimeFilter refines the learned spatial-temporal dependencies by filtering out irrelevant correlations while preserving the most critical ones in a patch-specific manner. Extensive experiments on 13 real-world datasets from diverse application domains demonstrate the state-of-the-art performance of TimeFilter. The code is available at https://github.com/TROUBADOUR000/TimeFilter.

Non-stationarity poses significant challenges for multivariate time series forecasting due to the inherent short-term fluctuations and long-term trends that can lead to spurious regressions or obscure essential long-term relationships. Most existing methods either eliminate or retain non-stationarity without adequately addressing its distinct impacts on short-term and long-term modeling. Eliminating non-stationarity is essential for avoiding spurious regressions and capturing local dependencies in short-term modeling, while preserving it is crucial for revealing long-term cointegration across variates. In this paper, we propose TimeBridge, a novel framework designed to bridge the gap between non-stationarity and dependency modeling in long-term time series forecasting. By segmenting input series into smaller patches, TimeBridge applies Integrated Attention to mitigate short-term non-stationarity and capture stable dependencies within each variate, while Cointegrated Attention preserves non-stationarity to model long-term cointegration across variates. Extensive experiments show that TimeBridge consistently achieves state-of-the-art performance in both short-term and long-term forecasting. Additionally, TimeBridge demonstrates exceptional performance in financial forecasting on the CSI 500 and S&P 500 indices, further validating its robustness and effectiveness. Code is available at https://github.com/Hank0626/TimeBridge.

High-frequency algorithmic trading has consistently attracted attention in both academic and industrial fields, which is formally modeled as a near real-time sequential decision problem. DRL methods are treated as a promising direction compared with the traditional approaches, as they have shown great potential in chasing maximum accumulative return. However, the financial data gathered from volatile market change rapidly, which makes it dramatically difficult to grasp crucial factors for effective decision-making. Existing works mainly focus on capturing temporal relations while ignoring deriving essential factors across features. Therefore, we propose a DRL-based cross-contextual sequential optimization (CCSO) method for algorithmic trading. In particular, we employ a convolution module in the first stage to derive latent factors via inter-sequence aggregation and apply a well-designed self-attention module in the second stage to capture market dynamics by aggregating temporal intra-sequence details. With the two-stage extractor as encoder and a RNN-based decision-maker as decoder, an Encoder-Decoder module is established as the policy network to conduct potent feature analysis and suggest action plans. Then, we design a dynamic programming based learning method to address the challenge of complex network updates in reinforcement learning, leading to considerable enhancement in learning stability and efficiency. To the best of our knowledge, this is the first work that solves the sequential optimization problem by joint representation of trading data across time and features in the DRL framework. Extensive experiments demonstrate the superior performance of our method compared to other state-of-the-art algorithmic trading approaches in various widely-used metrics.

Stock price prediction is a challenging problem in the field of finance and receives widespread attention. In recent years, with the rapid development of technologies such as deep learning and graph neural networks, more research methods have begun to focus on exploring the interrelationships between stocks. However, existing methods mostly focus on the short-term dynamic relationships of stocks and directly integrating relationship information with temporal information. They often overlook the complex nonlinear dynamic characteristics and potential higher-order interaction relationships among stocks in the stock market. Therefore, we propose a stock price trend prediction model named LSR-IGRU in this paper, which is based on long short-term stock relationships and an improved GRU input. Firstly, we construct a long short-term relationship matrix between stocks, where secondary industry information is employed for the first time to capture long-term relationships of stocks, and overnight price information is utilized to establish short-term relationships. Next, we improve the inputs of the GRU model at each step, enabling the model to more effectively integrate temporal information and long short-term relationship information, thereby significantly improving the accuracy of predicting stock trend changes. Finally, through extensive experiments on multiple datasets from stock markets in China and the United States, we validate the superiority of the proposed LSR-IGRU model over the current state-of-the-art baseline models. We also apply the proposed model to the algorithmic trading system of a financial company, achieving significantly higher cumulative portfolio returns compared to other baseline methods. Our sources are released at https://github.com/ZP1481616577/Baselines\_LSR-IGRU.