WaveletMamba: Harnessing learnable multi-scale state space dynamics for time series forecasting.

Abstract

Multivariate time series forecasting requires models capable of capturing complex temporal dependencies across multiple variates and time scales. Although Transformer-based architectures have demonstrated strong performance in modeling long-range dependencies, their ability to jointly represent multiscale temporal patterns remains limited. To address this issue, this paper proposes WaveletMamba, a novel forecasting framework that integrates two newly designed components: the Multi-Scale Haar Module (MSHM) and the Temporal Mamba Refinement (TMR) block. The MSHM block learns multiscale Haar-like representations by extracting both low- and high-frequency components, enabling effective modeling of local and global temporal features. These multiscale representations are subsequently fused by the TMR block, which incorporates a bi-scanning Mamba mechanism to enhance modeling of long-range temporal dependencies and cross-variable interactions. Extensive experiments across 13 standard time series forecasting benchmark datasets demonstrate that WaveletMamba consistently achieves predictive performance comparable to or superior to existing Mamba and Transformer-based methods, particularly in long-horizon forecasting. Furthermore, the proposed model exhibits improved generalization across diverse variates and better utilization of arbitrary lookback windows, making it a strong alternative as the fundamental Mamba-based backbone of time series forecasting.