Developments in Deep Learning have significantly improved time series forecasting by enabling more accurate modeling of complex temporal dependencies inherent in sequential data. The effectiveness of such models is often demonstrated on limited sets of specific real-world data. Although this allows for comparative analysis, it still does not demonstrate how specific data characteristics align with the architectural strengths of individual models. Our research aims at uncovering clear connections between time series characteristics and particular models. We introduce a novel dataset generated using Gaussian Processes, specifically designed to display distinct, known characteristics for targeted evaluations of model adaptability to them. Furthermore, we present TimeFlex, a new model that incorporates a modular architecture tailored to handle diverse temporal dynamics, including trends and periodic patterns. This model is compared to current state-of-the-art models, offering a deeper understanding of how models perform under varied time series conditions.

Time series, typically represented as numerical sequences, can also be transformed into images and texts, offering multi-modal views (MMVs) of the same underlying signal. These MMVs can reveal complementary patterns and enable the use of powerful pre-trained large models, such as large vision models (LVMs), for long-term time series forecasting (LTSF). However, as we identified in this work, the state-of-the-art (SOTA) LVM-based forecaster poses an inductive bias towards "forecasting periods". To harness this bias, we propose DMMV, a novel decomposition-based multi-modal view framework that leverages trend-seasonal decomposition and a novel backcast-residual based adaptive decomposition to integrate MMVs for LTSF. Comparative evaluations against 14 SOTA models across diverse datasets show that DMMV outperforms single-view and existing multi-modal baselines, achieving the best mean squared error (MSE) on 6 out of 8 benchmark datasets. The code for this paper is available at: https://github.com/D2I-Group/dmmv.

Time series forecasting and anomaly detection are common tasks for practitioners in industries such as retail, manufacturing, advertising and energy. Two unique challenges stand out: (1) efficiently and accurately forecasting time series or detecting anomalies in large volumes automatically; and (2) ensuring interpretability of results to effectively incorporate business insights. We present ARIMA_PLUS, a novel framework to overcome these two challenges by a unique combination of (a) accurate and interpretable time series models and (b) scalable and fully managed system infrastructure. The model has a sequential and modular structure to handle different components of the time series, including holiday effects, seasonality, trend, and anomalies, which enables high interpretability of the results. Novel enhancements are made to each module, and a unified framework is established to address both forecasting and anomaly detection tasks simultaneously. In terms of accuracy, its comprehensive benchmark on the 42 public datasets in the Monash forecasting repository shows superior performance over not only well-established statistical alternatives (such as ETS, ARIMA, TBATS, Prophet) but also newer neural network models (such as DeepAR, N-BEATS, PatchTST, TimeMixer). In terms of infrastructure, it is directly built into the query engine of BigQuery in Google Cloud. It uses a simple SQL interface and automates tedious technicalities such as data cleaning and model selection. It automatically scales with managed cloud computational and storage resources, making it possible to forecast 100 million time series using only 1.5 hours with a throughput of more than 18000 time series per second. In terms of interpretability, we present several case studies to demonstrate time series insights it generates and customizability it offers.

Time series forecasting holds significant value in various domains such as economics, traffic, energy, and AIOps, as accurate predictions facilitate informed decision-making. However, the existing Mean Squared Error (MSE) loss function sometimes fails to accurately capture the seasonality or trend within the forecasting horizon, even when decomposition modules are used in the forward propagation to model the trend and seasonality separately. To address these challenges, we propose a simple yet effective Decomposition-Based Loss function called DBLoss. This method uses exponential moving averages to decompose the time series into seasonal and trend components within the forecasting horizon, and then calculates the loss for each of these components separately, followed by weighting them. As a general loss function, DBLoss can be combined with any deep learning forecasting model. Extensive experiments demonstrate that DBLoss significantly improves the performance of state-of-the-art models across diverse real-world datasets and provides a new perspective on the design of time series loss functions.

In the evolution of Intelligent Transportation Systems (ITS), traffic flow prediction has played a pivotal role [1]. Accurate and real-time traffic forecasting is not only a fundamental component of ITS but also a key enabler for efficient urban operation and intelligent mobility development [2, 3]. With the rapid increase in private vehicle ownership, particularly in fast-growing economies, urban road networks have become increasingly congested, and major intersections and arterial roads often experience persistent traffic jams [4]. By accurately predicting traffic flow over short time intervals at critical intersections, transportation authorities can make informed decisions on traffic control and road planning, reduce accidents and delays, and provide travelers with reasonable route recommendations, thereby alleviating traffic pressure and maximizing the utilization of road resources. Figure 1 shows the traffic flow distribution scene at a typical four-way intersection on a city road. In traditional traffic flow prediction studies, various modeling approaches have been proposed, ranging from classical time series models (such as ARIMA) to machine learning and deep learning frameworks (such as RNN and LSTM) [5]. Although these single-model approaches can achieve satisfactory planning performance under controlled conditions [6], their generalization and robustness are often limited by the highly dynamic and nonlinear nature of urban traffic systems [7]. Moreover, most existing models primarily emphasize prediction accuracy while overlooking critical aspects such as computational efficiency, adaptability, and scalability, which are essential for real-time applications in large-scale traffic networks [8]. To address the aforementioned limitations, hybrid and decomposition-based modeling approaches have attracted growing research interest.

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.

Multivariate long-term and efficient time series forecasting is a key requirement for a variety of practical applications, and there are complex interleaving time dynamics in time series data that require decomposition modeling. Traditional time series decomposition methods are single and rely on fixed rules, which are insufficient for mining the potential information of the series and adapting to the dynamic characteristics of complex series. On the other hand, the Transformer-based models for time series forecasting struggle to effectively model long sequences and intricate dynamic relationships due to their high computational complexity. To overcome these limitations, we introduce KARMA, with an Adaptive Time Channel Decomposition module (ATCD) to dynamically extract trend and seasonal components. It further integrates a Hybrid Frequency-Time Decomposition module (HFTD) to further decompose Series into frequency-domain and time-domain. These components are coupled with multi-scale Mamba-based KarmaBlock to efficiently process global and local information in a coordinated manner. Experiments on eight real-world datasets from diverse domains well demonstrated that KARMA significantly outperforms mainstream baseline methods in both predictive accuracy and computational efficiency. Code and full results are available at this repository: https://github.com/yedadasd/KARMA

Rapid expansion of model size has emerged as a key challenge in time series forecasting. From early Transformer with tens of megabytes to recent architectures like TimesNet with thousands of megabytes, performance gains have often come at the cost of exponentially increasing parameter counts. But is this scaling truly necessary? To question the applicability of the scaling law in time series forecasting, we propose Alinear, an ultra-lightweight forecasting model that achieves competitive performance using only k-level parameters. We introduce a horizon-aware adaptive decomposition mechanism that dynamically rebalances component emphasis across different forecast lengths, alongside a progressive frequency attenuation strategy that achieves stable prediction in various forecasting horizons without incurring the computational overhead of attention mechanisms. Extensive experiments on seven benchmark datasets demonstrate that Alinear consistently outperforms large-scale models while using less than 1% of their parameters, maintaining strong accuracy across both short and ultra-long forecasting horizons. Moreover, to more fairly evaluate model efficiency, we propose a new parameter-aware evaluation metric that highlights the superiority of ALinear under constrained model budgets. Our analysis reveals that the relative importance of trend and seasonal components varies depending on data characteristics rather than following a fixed pattern, validating the necessity of our adaptive design. This work challenges the prevailing belief that larger models are inherently better and suggests a paradigm shift toward more efficient time series modeling.

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.