Forecasting real-world time series requires modeling both short-term fluctuations and long-term evolutions, as these signals typically exhibit multiscale temporal structures. A core challenge lies in reconciling such dynamics: high-frequency seasonality demands local precision, while low-frequency trends require global robustness. However, most existing methods adopt a unified loss function across all temporal components, overlooking their structural differences. This misalignment often causes overfitting to seasonal noise or underfitting of long-term trends, leading to suboptimal forecasting performance. To address this issue, we propose a Physics-guided Multiscale Loss Framework (PMLF) that decomposes time series into seasonal and trend components and assigns component-specific objectives grounded in the distinct energy responses of oscillatory and drift dynamics. Specifically, we assign a quadratic loss to seasonal components, reflecting the quadratic potential energy profile of molecular vibration, while a logarithmic loss is used for trend components to capture the sublinear energy profile of molecular drift under sustained external forces. Furthermore, we introduce a softmax-based strategy that adaptively balances the unequal energetic responses of these two physical processes. Experiments on different public benchmarks show that PMLF improves the performance of diverse baselines, demonstrating the effectiveness of physics-guided loss design in modeling structural heterogeneity in time series forecasting.

Time series forecasting is crucial for various applications, such as weather, traffic, electricity, and energy predictions. Currently, common time series forecasting methods are based on Transformers. However, existing approaches primarily model limited time series or fixed scales, making it more challenging to capture diverse features cross different ranges. Additionally, traditional methods like STL for complex seasonality-trend decomposition require pre-specified seasonal periods and typically handle only single, fixed seasonality. We propose the Hybrid Decomposition Dual-Stream Adaptive Transformer (DSAT-HD), which integrates three key innovations to address the limitations of existing methods: 1) A hybrid decomposition mechanism combining EMA and Fourier decomposition with RevIN normalization, dynamically balancing seasonal and trend components through noise Top-k gating; 2) A multi-scale adaptive pathway leveraging a sparse allocator to route features to four parallel Transformer layers, followed by feature merging via a sparse combiner, enhanced by hybrid attention combining local CNNs and global interactions; 3) A dual-stream residual learning framework where CNN and MLP branches separately process seasonal and trend components, coordinated by a balanced loss function minimizing expert collaboration variance. Extensive experiments on nine datasets demonstrate that DSAT-HD outperforms existing methods overall and achieves state-of-the-art performance on some datasets. Notably, it also exhibits stronger generalization capabilities across various transfer scenarios.

Abstract:In the metro intelligent transportation system, accurate transfer passenger flow prediction is a key link in optimizing operation plans and improving transportation efficiency. To further improve the theory of metro internal transfer passenger flow prediction and provide more reliable support for intelligent operation decisions, this paper innovatively proposes a metro transfer passenger flow prediction model that integrates the Seasonal and Trend decomposition using Loess (STL) method and Gated Recurrent Unit (GRU).In practical application, the model first relies on the deep learning library Keras to complete the construction and training of the GRU model, laying the foundation for subsequent prediction; then preprocesses the original metro card swiping data, uses the graph-based depth-first search algorithm to identify passengers' travel paths, and further constructs the transfer passenger flow time series; subsequently adopts the STL time series decomposition algorithm to decompose the constructed transfer p assenger flow time series into trend component, periodic component and residual component, and uses the 3σ principle to eliminate and fill the outliers in the residual component, and finally completes the transfer passenger flow prediction.Taking the trans fer passenger flow data of a certain metro station as the research sample, the validity of the model is verified. The results show that compared with Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and the combined model of STL time series decom position method and Long Short-Term Memory (STL-LSTM), the STL-GRU combined prediction model significantly improves the prediction accuracy of transfer passenger flow on weekdays (excluding Fridays), Fridays and rest days, with the mean absolute percentage error (MAPE) of the prediction results reduced by at least 2.3, 1.36 and 6.42 percentage points respectively. This study focuses on the field of metro transfer passenger flow prediction, aiming to break through existing technical bottlenecks through the construction of an innovative model and provide more accurate decision -making basis for metro operation management. Transfer stations, as passenger flow distribution hubs, their flow dynamics are directly related to operational efficiency and service quality.

Forecasting complex time series is an important yet challenging problem that involves various industrial applications. Recently, masked time-series modeling has been proposed to effectively model temporal dependencies for forecasting by reconstructing masked segments from unmasked ones. However, since the semantic information in time series is involved in intricate temporal variations generated by multiple time series components, simply masking a raw time series ignores the inherent semantic structure, which may cause MTM to learn spurious temporal patterns present in the raw data. To capture distinct temporal semantics, we show that masked modeling techniques should address entangled patterns through a decomposition approach. Specifically, we propose ST-MTM, a masked time-series modeling framework with seasonal-trend decomposition, which includes a novel masking method for the seasonal-trend components that incorporates different temporal variations from each component. ST-MTM uses a period masking strategy for seasonal components to produce multiple masked seasonal series based on inherent multi-periodicity and a sub-series masking strategy for trend components to mask temporal regions that share similar variations. The proposed masking method presents an effective pre-training task for learning intricate temporal variations and dependencies. Additionally, ST-MTM introduces a contrastive learning task to support masked modeling by enhancing contextual consistency among multiple masked seasonal representations. Experimental results show that our proposed ST-MTM achieves consistently superior forecasting performance compared to existing masked modeling, contrastive learning, and supervised forecasting methods.

Long-term time series forecasting (LTSF) offers broad utility in practical settings like energy consumption and weather prediction. Accurately predicting long-term changes, however, is demanding due to the intricate temporal patterns and inherent multi-scale variations within time series. This work confronts key issues in LTSF, including the suboptimal use of multi-granularity information, the neglect of channel-specific attributes, and the unique nature of trend and seasonal components, by introducing a proficient MLP-based forecasting framework. Our method adeptly disentangles complex temporal dynamics using clear, concurrent predictions across various scales. These multi-scale forecasts are then skillfully integrated through a system that dynamically assigns importance to information from different granularities, sensitive to individual channel characteristics. To manage the specific features of temporal patterns, a two-pronged structure is utilized to model trend and seasonal elements independently. Experimental results on eight LTSF benchmarks demonstrate that MDMixer improves average MAE performance by 4.64% compared to the recent state-of-the-art MLP-based method (TimeMixer), while achieving an effective balance between training efficiency and model interpretability.

In long-term time series forecasting, Transformer-based models have achieved great success, due to its ability to capture long-range dependencies. However, existing transformer-based methods face challenges in accurately identifying which variables play a pivotal role in the prediction process and tend to overemphasize noisy channels, thereby limiting the interpretability and practical effectiveness of the models. Besides, it faces scalability issues due to quadratic computational complexity of self-attention. In this paper, we propose a new model named Inverted Seasonal-Trend Decomposition Transformer (Ister), which addresses these challenges in long-term multivariate time series forecasting by designing an improved Transformer-based structure. Ister firstly decomposes original time series into seasonal and trend components. Then we propose a new Dot-attention mechanism to process the seasonal component, which improves both accuracy, computation complexity and interpretability. Upon completion of the training phase, it allows users to intuitively visualize the significance of each feature in the overall prediction. We conduct comprehensive experiments, and the results show that Ister achieves state-of-the-art (SOTA) performance on multiple datasets, surpassing existing models in long-term prediction tasks.

Time series forecasting is vital in numerous web applications, influencing critical decision-making across industries. While diffusion models have recently gained increasing popularity for this task, we argue they suffer from a significant drawback: indiscriminate noise addition to the original time series followed by denoising, which can obscure underlying dynamic evolving trend and complicate forecasting. To address this limitation, we propose a novel flexible decoupled framework (FDF) that learns high-quality time series representations for enhanced forecasting performance. A key characteristic of our approach leverages the inherent inductive bias of time series data of its decomposed trend and seasonal components, each modeled separately to enable decoupled analysis and modeling. Specifically, we propose an innovative Conditional Denoising Seasonal Module (CDSM) within the diffusion model, which leverages statistical information from the historical window to conditionally model the complex seasonal component. Notably, we incorporate a Polynomial Trend Module (PTM) to effectively capture the smooth trend component, thereby enhancing the model's ability to represent temporal dependencies. Extensive experiments validate the effectiveness of our framework, demonstrating superior performance over existing methods and highlighting its flexibility in time series forecasting. The source code is available at https://github.com/zjt-gpu/FDF.

Recently, there has been a growing interest in Long-term Time Series Forecasting (LTSF), which involves predicting long-term future values by analyzing a large amount of historical time-series data to identify patterns and trends. There exist significant challenges in LTSF due to its complex temporal dependencies and high computational demands. Although Transformer-based models offer high forecasting accuracy, they are often too compute-intensive to be deployed on devices with hardware constraints. On the other hand, the linear models aim to reduce the computational overhead by employing either decomposition methods in the time domain or compact representations in the frequency domain. In this paper, we propose MixLinear, an ultra-lightweight multivariate time series forecasting model specifically designed for resource-constrained devices. MixLinear effectively captures both temporal and frequency domain features by modeling intra-segment and inter-segment variations in the time domain and extracting frequency variations from a low-dimensional latent space in the frequency domain. By reducing the parameter scale of a downsampled $n$-length input/output one-layer linear model from $O(n^2)$ to $O(n)$, MixLinear achieves efficient computation without sacrificing accuracy. Extensive evaluations with four benchmark datasets show that MixLinear attains forecasting performance comparable to, or surpassing, state-of-the-art models with significantly fewer parameters ($0.1K$), which makes it well-suited for deployment on devices with limited computational capacity.

eBay partners with external vendors, which allows customers to freely select a vendor to complete their eBay experiences. However, vendor outages can hinder customer experiences. Consequently, eBay can disable a problematic vendor to prevent customer loss. Disabling the vendor too late risks losing customers willing to switch to other vendors, while disabling it too early risks losing those unwilling to switch. In this paper, we propose a data-driven solution to answer whether eBay should disable a problematic vendor and when to disable it. Our solution involves forecasting customer behavior. First, we use a multiplicative seasonality model to represent behavior if all vendors are fully functioning. Next, we use a Monte Carlo simulation to represent behavior if the problematic vendor remains enabled. Finally, we use a linear model to represent behavior if the vendor is disabled. By comparing these forecasts, we determine the optimal time for eBay to disable the problematic vendor.

A common issue for machine learning models applied to time-series forecasting is the temporal evolution of the data distributions (i.e., concept drift). Because most of the training data does not reflect such changes, the models present poor performance on the new out-of-distribution scenarios and, therefore, the impact of such events cannot be reliably anticipated ahead of time. We present and publicly release CounterfacTS, a tool to probe the robustness of deep learning models in time-series forecasting tasks via counterfactuals. CounterfacTS has a user-friendly interface that allows the user to visualize, compare and quantify time series data and their forecasts, for a number of datasets and deep learning models. Furthermore, the user can apply various transformations to the time series and explore the resulting changes in the forecasts in an interpretable manner. Through example cases, we illustrate how CounterfacTS can be used to i) identify the main features characterizing and differentiating sets of time series, ii) assess how the model performance depends on these characateristics, and iii) guide transformations of the original time series to create counterfactuals with desired properties for training and increasing the forecasting performance in new regions of the data distribution. We discuss the importance of visualizing and considering the location of the data in a projected feature space to transform time-series and create effective counterfactuals for training the models. Overall, CounterfacTS aids at creating counterfactuals to efficiently explore the impact of hypothetical scenarios not covered by the original data in time-series forecasting tasks.