Non-Stationary Time Series Forecasting Based on Fourier Analysis and Cross Attention Mechanism

TL;DR

This work tackles non-stationary time-series forecasting by introducing AEFIN, a cross-attention–based framework that separates stable and unstable components and fuses them through a cross-attention mechanism. It combines a Fourier Analysis Network with an MLP to better capture seasonal and trend information, and it employs a composite loss that enforces stability in both time and frequency domains. Empirical results across multiple datasets show substantial improvements in MSE and MAE, especially under non-stationary conditions, underscoring the method's robustness and practical value for finance, weather, and traffic forecasting. The approach advances time-series modeling by explicitly handling inter-component dependencies and leveraging spectral information for stable trend extraction, offering a scalable path toward more reliable non-stationary forecasting.

Abstract

Time series forecasting has important applications in financial analysis, weather forecasting, and traffic management. However, existing deep learning models are limited in processing non-stationary time series data because they cannot effectively capture the statistical characteristics that change over time. To address this problem, this paper proposes a new framework, AEFIN, which enhances the information sharing ability between stable and unstable components by introducing a cross-attention mechanism, and combines Fourier analysis networks with MLP to deeply explore the seasonal patterns and trend characteristics in unstable components. In addition, we design a new loss function that combines time-domain stability constraints, time-domain instability constraints, and frequency-domain stability constraints to improve the accuracy and robustness of forecasting. Experimental results show that AEFIN outperforms the most common models in terms of mean square error and mean absolute error, especially under non-stationary data conditions, and shows excellent forecasting capabilities. This paper provides an innovative solution for the modeling and forecasting of non-stationary time series data, and contributes to the research of deep learning for complex time series.

Figures (6)

• Figure 1: The original sequence, unstable components, and stable components at the first 100 time lengths in ExchangeRate dataset.
• Figure 2: The overall architecture of our model AEFIN. $X_t$ is the input data, the blue arrow is the direction of data flow, the blue dashed line indicates the direction of flow of the data used for residual connection, and the black arrow indicates the source of the data in the loss function.
• Figure 3: True and predicted values when the forecasting length is 96.
• Figure 4: True and predicted values when the forecasting length is 168.
• Figure 5: True and predicted values when the forecasting length is 720.