Deep learning models have progressively advanced time series forecasting due to their powerful capacity in capturing sequence dependence. Nevertheless, it is still challenging to make accurate predictions due to the existence of non-stationarity in real-world data, denoting the data distribution rapidly changes over time. To mitigate such a dilemma, several efforts have been conducted by reducing the non-stationarity with normalization operation. However, these methods typically overlook the distribution discrepancy between the input series and the horizon series, and assume that all time points within the same instance share the same statistical properties, which is too ideal and may lead to suboptimal relative improvements. To this end, we propose a novel slice-level adaptive normalization, referred to \textbf{SAN}, which is a novel scheme for empowering time series forecasting with more flexible normalization and denormalization.

Time series forecasting plays a vital role in critical domains like energy and transportation, where non-stationary dynamics are deeply intertwined with events in other modalities such as texts. However, incorporating natural language-based external events to improve non-stationary forecasting remains largely unexplored, as most approaches still rely on a single modality, resulting in limited contextual knowledge and model underperformance. Enabling fine-grained multimodal interactions between temporal and textual data is challenged by three fundamental issues: (1) the difficulty of fine-grained synchronization between time-varying discrete textual events and continuous time series; (2) the inherent temporal uncertainty introduced by textual semantics; and (3) the misalignment between textual event embeddings and multi-resolution temporal patterns. In this work, we address these challenges by introducing event-aware non-stationary time series forecasting (EventTSF), an autoregressive generation framework that integrates historical time series with textual events to make subsequent forecasts. Specifically, EventTSF uses autoregressive diffusion with flow matching at each step to capture nuanced temporal-event interactions. To handle event-induced uncertainty, flow matching timesteps are adaptively controlled according to event semantic signals. The underlying denoiser employs a multimodal U-shaped diffusion transformer that efficiently fuses temporal and textual modalities across different resolutions. Extensive experiments on 8 synthetic and real-world datasets show that EventTSF outperforms 12 baselines across diverse event-aware non-stationary time series forecasting scenarios, achieving substantial improvements of 10.7% higher forecasting accuracy and $1.13\times$ faster training efficiency.

Deep neural networks (DNNs) have recently achieved remarkable advancements in time series forecasting (TSF) due to their powerful ability of sequence dependence modeling. To date, existing DNN-based TSF methods still suffer from unreliable predictions for real-world data due to its non-stationarity characteristics, i.e., data distribution varies quickly over time. To mitigate this issue, several normalization methods (e.g., SAN) have recently been specifically designed by normalization in a fixed period/window in the time domain. However, these methods still struggle to capture distribution variations, due to the complex time patterns of time series in the time domain. Based on the fact that wavelet transform can decompose time series into a linear combination of different frequencies, which exhibits distribution variations with time-varying periods, we propose a novel Dual-domain Dynamic Normalization (DDN) to dynamically capture distribution variations in both time and frequency domains.

Time series forecasting typically needs to address non-stationary data with evolving trend and seasonal patterns. To address the non-stationarity, reversible instance normalization has been recently proposed to alleviate impacts from the trend with certain statistical measures, e.g., mean and variance. Although they demonstrate improved predictive accuracy, they are limited to expressing basic trends and are incapable of handling seasonal patterns. To address this limitation, this paper proposes a new instance normalization solution, called frequency adaptive normalization (FAN), which extends instance normalization in handling both dynamic trend and seasonal patterns. Specifically, we employ the Fourier transform to identify instance-wise predominant frequent components that cover most non-stationary factors.

Non-stationarity is an intrinsic property of real-world time series and plays a crucial role in time series forecasting. Previous studies primarily adopt instance normalization to attenuate the non-stationarity of original series for better predictability. However, instance normalization that directly removes the inherent non-stationarity can lead to three issues: (1) disrupting global temporal dependencies, (2) ignoring channel-specific differences, and (3) producing over-smoothed predictions. To address these issues, we theoretically demonstrate that variance can be a valid and interpretable proxy for quantifying non-stationarity of time series. Based on the analysis, we propose a novel lightweight \textit{C}hannel-wise \textit{D}ynamic \textit{F}usion \textit{M}odel (\textit{CDFM}), which selectively and dynamically recovers intrinsic non-stationarity of the original series, while keeping the predictability of normalized series. First, we design a Dual-Predictor Module, which involves two branches: a Time Stationary Predictor for capturing stable patterns and a Time Non-stationary Predictor for modeling global dynamics patterns. Second, we propose a Fusion Weight Learner to dynamically characterize the intrinsic non-stationary information across different samples based on variance. Finally, we introduce a Channel Selector to selectively recover non-stationary information from specific channels by evaluating their non-stationarity, similarity, and distribution consistency, enabling the model to capture relevant dynamic features and avoid overfitting. Comprehensive experiments on seven time series datasets demonstrate the superiority and generalization capabilities of CDFM.

Deep learning models have progressively advanced time series forecasting due to their powerful capacity in capturing sequence dependence. Nevertheless, it is still challenging to make accurate predictions due to the existence of non-stationarity in real-world data, denoting the data distribution rapidly changes over time. To mitigate such a dilemma, several efforts have been conducted by reducing the non-stationarity with normalization operation. However, these methods typically overlook the distribution discrepancy between the input series and the horizon series, and assume that all time points within the same instance share the same statistical properties, which is too ideal and may lead to suboptimal relative improvements. To this end, we propose a novel slice-level adaptive normalization, referred to \textbf{SAN}, which is a novel scheme for empowering time series forecasting with more flexible normalization and denormalization.

Despite their popularity, deep neural networks (DNNs) applied to time series forecasting often fail to beat simpler statistical models. One of the main causes of this suboptimal performance is the data non-stationarity present in many processes. In particular, changes in the mean and variance of the input data can disrupt the predictive capability of a DNN. In this paper, we first show how DNN forecasting models fail in simple non-stationary settings. We then introduce GAS-Norm, a novel methodology for adaptive time series normalization and forecasting based on the combination of a Generalized Autoregressive Score (GAS) model and a Deep Neural Network. The GAS approach encompasses a score-driven family of models that estimate the mean and variance at each new observation, providing updated statistics to normalize the input data of the deep model. The output of the DNN is eventually denormalized using the statistics forecasted by the GAS model, resulting in a hybrid approach that leverages the strengths of both statistical modeling and deep learning. The adaptive normalization improves the performance of the model in non-stationary settings. The proposed approach is model-agnostic and can be applied to any DNN forecasting model. To empirically validate our proposal, we first compare GAS-Norm with other state-of-the-art normalization methods. We then combine it with state-of-the-art DNN forecasting models and test them on real-world datasets from the Monash open-access forecasting repository. Results show that deep forecasting models improve their performance in 21 out of 25 settings when combined with GAS-Norm compared to other normalization methods.