Frequency Adaptive Normalization For Non-stationary Time Series Forecasting

TL;DR

This paper introduces Frequency Adaptive Normalization (FAN), a novel method that enhances non-stationary time series forecasting by modeling both trend and seasonal patterns through Fourier analysis, significantly improving prediction accuracy.

Contribution

FAN extends instance normalization by incorporating Fourier transform to handle seasonal patterns, providing a model-agnostic solution for non-stationary time series forecasting.

Findings

FAN achieves 7.76% to 37.90% average MSE improvements.

FAN effectively models both trend and seasonal components.

FAN is applicable to various forecasting models.

Abstract

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. Furthermore, the discrepancy of those frequency components between inputs and outputs is explicitly modeled as a prediction task with a simple MLP model. FAN is a model-agnostic method that can be applied to arbitrary predictive backbones. We instantiate FAN on four widely used forecasting models as the backbone and evaluate their prediction performance improvements on eight benchmark datasets. FAN demonstrates significant performance advancement, achieving 7.76% ~ 37.90% average improvements in MSE.