Frequency Adaptive Normalization For Non-stationary Time Series Forecasting

TL;DR

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 and is a model-agnostic method that can be applied to arbitrary predictive backbones.

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.

Figures (12)

• Figure 1: A sinusoidal signal with linearly varying frequency which is a common example of a non-stationary time series. In the lower-left corner, we plot the Fourier spectrum for three segments of the signal.
• Figure 2: An overview of FAN which consists of normalization, frequency residual learning, denormalization steps, and incorporates a prior loss for non-stationary patterns.
• Figure 3: Visualization of long-term 168 steps forecasting results of a test sample in Traffic dataset, using DLinear enhanced with different normalization methods.
• Figure 4: Comparison with other normalization methods. (a) ADF test after normalization, the smaller the value, the higher the stationarity. (b) Model efficiency comparison with SAN, including MSE/MAE, parameters (in millions), and training time per iteration (ms/100). (c) Performance in MSE vs. input length on the ETTm2 dataset.
• Figure 5: Frequency distributions vs. forecast error in MSE with different K and output length $H$.