PeriodPatch: A frequency-aware modular framework with patch-based embedding and periodic bias for multivariate time series forecasting.

Abstract

Multivariate time series forecasting is difficult due to complex temporal dynamics, inter-variable connections, and periodic structures. Patch-based architectures have shown promise, but they often fail to capture frequency-domain patterns or structural variety across time and variables. To fill these gaps, PeriodPatch (Period-Aware Patch-Based Forecasting) integrates frequency-aware and structure-sensitive design into the patching paradigm. PeriodPatch uses intra-patch convolution and a decomposition module to extract trend and residual components to improve local temporal representations. Prominent frequency components are extracted using Fourier transform with a Reference Signal Generator (RSGenerator) to generate temporal encoding reference signals. These references are merged utilizing controlled Periodic Embedding to add frequency-aligned positional bias to patch embeddings. Cross-attention selectively focuses on aligned periodic patterns to combine observed patch embeddings with frequency-informed reference sequences. Inter-Variable Learning attention weights for each variable strengthen multivariate representation with structural awareness by capturing dynamic cross-channel dependencies. PeriodPatch outperforms most baselines in accuracy and resilience across 11 benchmark datasets and four prediction periods. Compared to PatchTST, it reduces MSE and MAE by 13.1% and 11.7% for long-term prediction tasks and improves MSE and MAE by 25% and 20% for short-term tasks. PeriodPatch outperforms DLinear and transformer-based methods like Informer, Autoformer, FEDformer, and iTransformer. PeriodPatch identifies periodic structures and variable dependencies, making it a robust, interpretable, and generalizable multivariate time series forecasting method.