MFRS: A Multi-Frequency Reference Series Approach to Scalable and Accurate Time-Series Forecasting

TL;DR

MFRS tackles multivariate time-series forecasting by uncovering predictability through periodic components. It constructs multi-frequency Reference Series from dominant spectral components and harmonics, and uses an encoder-only Transformer with cross-attention between the original series and RS, guided by a synchronization mechanism and DC-aware normalization. Key contributions include the Base-Pattern Extractor, Reference-Series Generator, and Synchronous Alignment, enabling scalable forecasting with a small RS set. Empirical results on open and synthetic datasets show state-of-the-art performance and robustness to RS choices and look-back length, highlighting practical impact for scalable, frequency-aware forecasting.

Abstract

Multivariate time-series forecasting holds immense value across diverse applications, requiring methods to effectively capture complex temporal and inter-variable dynamics. A key challenge lies in uncovering the intrinsic patterns that govern predictability, beyond conventional designs, focusing on network architectures to explore latent relationships or temporal dependencies. Inspired by signal decomposition, this paper posits that time series predictability is derived from periodic characteristics at different frequencies. Consequently, we propose a novel time series forecasting method based on multi-frequency reference series correlation analysis. Through spectral analysis on long-term training data, we identify dominant spectral components and their harmonics to design base-pattern reference series. Unlike signal decomposition, which represents the original series as a linear combination of basis signals, our method uses a transformer model to compute cross-attention between the original series and reference series, capturing essential features for forecasting. Experiments on major open and synthetic datasets show state-of-the-art performance. Furthermore, by focusing on attention with a small number of reference series rather than pairwise variable attention, our method ensures scalability and broad applicability. The source code is available at: https://github.com/yuliang555/MFRS

Figures (10)

• Figure 1: MFRS architecture. The left part shows the process of generating RS, which differs between training and prediction stage. The right part represents the modeling based on invert Transformer.
• Figure 2: (a) spectrum $\Phi \left ( f \right )$, used for extracting HBP. (b) converted spectrum $\Psi \left ( \mathcal{T} \right )$, used for extracting PBP.
• Figure 3: synchronous alignment method. sliding observation $\mathbf{x}^{\left ( i \right )}$ along with training data $\mathbf{X}^{\left ( i \right )}$ and calculating their similarity denoted as corr. Taking the time step with the largest corr as parameter $\xi$.
• Figure 4: Compose with base-patterns $\mathcal{T} \in \left \{ 72, 36, 24, 18 \right \}$
• Figure 5: Compose with base-patterns $\mathcal{T} \in \left \{ 720, 360, 240, 180 \right \}$