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.
Time series forecasting, which aims to infer future values from temporal patterns of historical observations, plays a pivotal role in a wide range of real-world applications, such as transportation management (Cirstea et al. 2022), inventory optimization (Seyedan, Mafakheri, and Wang 2023), and climate modeling (Haq 2022). In recent years, various deep learning models based on diverse architectures-such as RNNs (Amalou, Mouhni, and Abdali 2022), CNNs (Mehtab and Sen 2022), Transformers (Woo et al. 2024), and MLPs (Zeng et al. 2023)-have gained significant attention and driven notable progress for time series forecasting (Lim and Zohren 2021). Despite these impressive advances, modeling time series remains fundamentally challenging due to the intrinsic complex nature of the real world, where temporal patterns unfold across multiple entangled scales, including long-term periodicity, short-term fluctuations, abrupt regime shifts, etc (Zhang et al. 2025a;Piao et al. 2024a). To tackle such complex temporal patterns, a compelling strategy is to leverage prior knowledge to decompose time series into trend and seasonal components (Wu et al. 2021;Zhou et al. 2022;Zeng et al. 2023), further enriched with multi-scale refinements that capture cross-scale interactions (Wang et al. 2024a), or into chunks with different period lengths (Wu et al. 2022). Concurrently, the frequency domain has emerged as a powerful alternative to conventional time-domain approaches by providing global view and energy compaction, two advantaged properties inaccessible in the time domain (Yi et al. 2023a), prompting a surge of interest in decomposing time series into high-and lowfrequency components (Piao et al. 2024b;Huang et al. 2025;Wu et al. 2025). Nevertheless, frequency-based decomposition remains fundamentally constrained in capturing timesensitive patterns that evolve dynamically over time. Surpassing the inherent limitations of pure time-or frequencydomain approaches, the wavelet domain is rapidly gaining momentum for its unique ability to unify time and frequency analysis, yielding multi-resolution and time-sensitive representations with strong localization across both domains (Guo et al. 2022).
However, wavelet-empowered forecasters are still suffering from a persistent bias toward recursively decomposing only low-frequency signals (i.e., approximation coefficients), rendering them particularly vulnerable to highfrequency signals (i.e., detail coefficients)-subtle yet informative components for accurately forecasting time series. Such bias severely undermines the full potential of the wavelet domain. To highlight the importance of highfrequency signals, Figure 1 (a) illustrates a two-level optimal subband tree guided by Shannon entropy. Although the high-frequency band d is typically underexplored by existing methods (Yi et al. 2024), it exhibits a high entropy of 1.24, suggesting the presence of rich structural information. Upon further decomposition of d, the component of dd still exhibits pronounced periodic patterns (see red circles), indicating that d retains entangled yet structured temporal patterns that merit deeper decomposition for more effective modeling. Additionally, the wavelet spectra of da and dd exhibit strong time-localized information (see Figure 1 (b)), on par with those observed in the aa ← a → ad branch. This observation further reinforces the necessity of deeper decomposition to isolate more informative time-frequency characteristics.
To address the aforementioned issues, we propose Wave-Tuner, a Wavelet decomposition framework empowered by full-spectrum subband Tuning for effective time series forecasting. The core idea of WaveTuner is to adaptively focus on high-frequency detail coefficients across multi-resolution wavelet subbands, facilitating the discovery of optimal subband routing patterns tailored to each time series input. Specifically, we introduce the Adaptive Wavelet Refinement (AWR) module, which transforms time series into time-frequency coefficients and utilizes an adaptive router to dynamically assign subband weights, enabling subbandspecific refinement that enhances the model’s ability to capture localized frequency dynamics. These coefficients are further refined to model inter-variable dependencies via hardware-friendly linear layers with residual connections, yielding finer time-frequency representations that empower WaveTuner to capture more informative and discriminative patterns across diverse spectral bands. Inspired by the exceptional data-fitting capacity of Kolmogorov-Arnold Networks (KAN), we design the Multi-branch Specialization (MBS) module, where each branch-instantiated as a KAN of different functional order-is specialized for a specific spectral band. This design aligns model complexity with frequency characteristics: low-frequency subbands benefit from smoother, low-order functions to capture global trends, while high-frequency subbands require higher-order expressiveness t
This content is AI-processed based on open access ArXiv data.