CANet: ChronoAdaptive Network for Enhanced Long-Term Time Series Forecasting under Non-Stationarity

TL;DR

CANet tackles non-stationarity in multivariate long-term time series forecasting by embedding a Non-stationary Adaptive Normalization (NSAN) module inside a CNN-based backbone, blending internal and external statistics via a Style Blending Gate and AdaIN to preserve non-stationary patterns and prevent over-stationarization. The approach is augmented with multi-resolution patching and a Stacked Kronecker Product Layer for efficiency, along with an Adaptive Spectral Block and Interactive Convolutional Block to handle noise and complex temporal dependencies. Across nine real-world benchmarks and horizons up to 720, CANet achieves substantial gains (up to 42% MSE and 22% MAE reductions) while using far fewer parameters and maintaining fast inference. Ablation studies confirm the critical role of NSAN and the integrated architectural components in delivering robust, scalable performance on non-stationary data.

Abstract

Long-term time series forecasting plays a pivotal role in various real-world applications. Despite recent advancements and the success of different architectures, forecasting is often challenging due to non-stationary nature of the real-world data, which frequently exhibit distribution shifts and temporal changes in statistical properties like mean and variance over time. Previous studies suggest that this inherent variability complicates forecasting, limiting the performance of many models by leading to loss of non-stationarity and resulting in over-stationarization (Liu, Wu, Wang and Long, 2022). To address this challenge, we introduce a novel architecture, ChoronoAdaptive Network (CANet), inspired by style-transfer techniques. The core of CANet is the Non-stationary Adaptive Normalization module, seamlessly integrating the Style Blending Gate and Adaptive Instance Normalization (AdaIN) (Huang and Belongie, 2017). The Style Blending Gate preserves and reintegrates non-stationary characteristics, such as mean and standard deviation, by blending internal and external statistics, preventing over-stationarization while maintaining essential temporal dependencies. Coupled with AdaIN, which dynamically adapts the model to statistical changes, this approach enhances predictive accuracy under non-stationary conditions. CANet also employs multi-resolution patching to handle short-term fluctuations and long-term trends, along with Fourier analysis-based adaptive thresholding to reduce noise. A Stacked Kronecker Product Layer further optimizes the model's efficiency while maintaining high performance. Extensive experiments on real-world datasets validate CANet's superiority over state-of-the-art methods, achieving a 42% reduction in MSE and a 22% reduction in MAE. The source code is publicly available at https://github.com/mertsonmezer/CANet.

Figures (6)

• Figure 1: Visualization of over-stationarization effects on the internal convolutional filter representations across four normalization methods, using identical model configurations trained on the Exchange dataset. (a)–(c) show that Layer, Batch, and Instance Normalization yield highly similar learned filters, consistent with their standardizing effect (see Lemma \ref{['lemma:over-stationarization']}). In contrast, (d) our NSAN learns a different filter configuration, reflecting the influence of its blended instance-specific statistics. This distinct internal parameterization aligns with NSAN's consistently superior ablation performance (see Table \ref{['tbl:ablation']}), supporting its role in mitigating over-stationarization and improving forecasting accuracy.
• Figure 2: The overall architecture of CANet. Instance Normalization encapsulates the base model, normalizing each input series and then denormalizing it right before output generation Kim2022. The NSAN module is employed to reintroduce diverse patterns associated with the non-stationary characteristics of time series data.
• Figure 3: The illustration of the Non-stationary Adaptive Normalization (NSAN) module, which integrates the Style Blending Gate with AdaIN to restore the non-stationary characteristics inherent in the original input time series. This module takes the mean and standard deviation as style properties and applies transformations through shifting and scaling operations, enabling the streaming matrix to adjust to changes in data distribution.
• Figure 4: Comparison of model complexity on the ETTm2 and Exchange datasets. Each model was tested with prediction length $O \in \{96, 192, 336, 720\}$, with the results averaged across these intervals.
• Figure 5: Model performance comparison across varying look-back windows $L \in \{24, 48, 96, 192, 336\}$ on the ETTm2 and Weather datasets, with a fixed prediction length $O = 96$ for each model.

Theorems & Definitions (1)

• Lemma 1