Multiple cyclicity and Wavelet Decomposition with Channel Correlation for Long-term Time Series Forecasting

Multivariate time series forecasting remains a challenge due to the complexity of local temporal dynamics and global dependencies across multiple variables. In this paper, we propose \textbf{N}eighboring \textbf{P}atching \textbf{Mixer} (\textbf{NPMixer}), a hierarchical architecture featuring a Learnable Stationary Wavelet Transform that adaptively learns filter coefficients to decompose signals into trend and detail components in a data-dependent manner. Our framework introduces a Neighboring Mixer Block that captures local temporal dynamics through a series of hierarchical MLP layers operating on non-overlapping patches. Specifically, the mixer block utilizes MLPs to learn temporal patterns within and across these patches, expanding the receptive field to capture multi-scale dependencies. A Channel-Mixing Encoder is applied to high-frequency components to learn channel correlations while preserving the stability of the underlying global trend. Extensive experiments on seven benchmark datasets demonstrate that NPMixer consistently outperforms state-of-the-art models, achieving better performance in 20 out of 28 ($71.4\%$) evaluated experimental setups for MSE.

Multivariate time series forecasting often struggles to capture long-range dependencies due to fixed lookback windows. Retrieval-augmented forecasting addresses this by retrieving historical segments from memory, but existing approaches rely on a channel-agnostic strategy that applies the same references to all variables. This neglects inter-variable heterogeneity, where different channels exhibit distinct periodicities and spectral profiles. We propose CRAFT (Channel-wise retrieval-augmented forecasting), a novel framework that performs retrieval independently for each channel. To ensure efficiency, CRAFT adopts a two-stage pipeline: a sparse relation graph constructed in the time domain prunes irrelevant candidates, and spectral similarity in the frequency domain ranks references, emphasizing dominant periodic components while suppressing noise. Experiments on seven public benchmarks demonstrate that CRAFT outperforms state-of-the-art forecasting baselines, achieving superior accuracy with practical inference efficiency.

Real-world time series are often governed by recurring patterns, but their dominant periods may vary across datasets, forecasting settings, and individual input windows. Existing cycle-aware forecasters commonly rely on a single period selected at the dataset level, which can be restrictive when periodic behavior changes over time or when multiple cycles coexist. Moreover, patch-based models typically process all patch positions uni- formly, although patches farther from the forecast boundary may require broader contextual refinement, while recent patches contain information that should be preserved more directly. Af- ter cyclic behavior is removed, the remaining dynamics may also span multiple temporal resolutions and cannot be adequately de- scribed at a single scale. We introduce CAMP, a Cycle-Aware Multi-Scale Patch Mixer designed to address these challenges. The Adaptive Cycle Learning module identifies dominant fre- quencies separately for each input window and generates both historical and future cyclic components without requiring a pre- defined cycle length. The Horizon-Guided Patch Mixer intro- duces position-dependent refinement, allowing earlier patches to incorporate broader temporal context while preserving infor- mation close to the forecast boundary. CAMP further models the de-cycled residual through temporally aligned multi-resolution representations, enabling complementary dynamics at different scales to be captured within one forecasting framework. Across seven long-term forecasting benchmarks, CAMP achieves the best average MSE on six datasets and the best or tied-best MAE on six. It also obtains the highest MSE win count across sixteen settings on four PEMS traffic benchmarks.