WaveTuner: Comprehensive Wavelet Subband Tuning for Time Series Forecasting

TL;DR

WaveTuner addresses multi-scale patterns in real-world time series by leveraging full-spectrum wavelet subbands. It introduces Adaptive Wavelet Refinement to adaptively weight subbands and Wave Embedding to capture inter-variable dependencies, plus Multi-Branch Specialization using Kolmogorov-Arnold Networks with frequency-aware orders. Across eight real-world datasets, WaveTuner achieves state-of-the-art forecasting performance, outperforming both time-domain and prior wavelet-based methods. The approach provides interpretable frequency-wise contributions and linear-time complexity, enabling effective long-horizon forecasting in practice.

Abstract

Due to the inherent complexity, temporal patterns in real-world time series often evolve across multiple intertwined scales, including long-term periodicity, short-term fluctuations, and abrupt regime shifts. While existing literature has designed many sophisticated decomposition approaches based on the time or frequency domain to partition trend-seasonality components and high-low frequency components, an alternative line of approaches based on the wavelet domain has been proposed to provide a unified multi-resolution representation with precise time-frequency localization. However, most wavelet-based methods suffer from a persistent bias toward recursively decomposing only low-frequency components, severely underutilizing subtle yet informative high-frequency components that are pivotal for precise time series forecasting. To address this problem, we propose WaveTuner, a Wavelet decomposition framework empowered by full-spectrum subband Tuning for time series forecasting. Concretely, WaveTuner comprises two key modules: (i) Adaptive Wavelet Refinement module, that transforms time series into time-frequency coefficients, utilizes an adaptive router to dynamically assign subband weights, and generates subband-specific embeddings to support refinement; and (ii) Multi-Branch Specialization module, that employs multiple functional branches, each instantiated as a flexible Kolmogorov-Arnold Network (KAN) with a distinct functional order to model a specific spectral subband. Equipped with these modules, WaveTuner comprehensively tunes global trends and local variations within a unified time-frequency framework. Extensive experiments on eight real-world datasets demonstrate WaveTuner achieves state-of-the-art forecasting performance in time series forecasting.

Figures (6)

• Figure 1: The critical role of analyzing high-frequency components in wavelet decomposition.
• Figure 2: Framework of WaveTuner, composed of Adaptive Wavelet Refinement (AWR) and Multi-Branch Specialization (MBS). AWR applies wavelet packet decomposition, adaptive frequency-aware weighting, and wave embedding to highlight informative subbands. MBS assigns specialized branches to each band for frequency-specific modeling. Finally, the head module maps the results to the prediction horizon before reconstruction via inverse wavelet packet transform.
• Figure 3: Visualization of learned weight.
• Figure 4: Visualization of predictions on the ETTh1 dataset with lookback and horizon length as 96.
• Figure 5: Decomposition visualization of the prediction.