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MMFNet: Multi-Scale Frequency Masking Neural Network for Multivariate Time Series Forecasting

Aitian Ma, Dongsheng Luo, Mo Sha

TL;DR

MMFNet tackles long-term multivariate time series forecasting by introducing a Multi-scale Masked Frequency Transformation (MMFT) that decomposes sequences at fine, intermediate, and coarse scales, applies learnable masks in the frequency domain, and reconstructs forecasts via spectral inversion. The approach directly addresses non-stationarity and local temporal variations while maintaining computational efficiency through frequency-domain operations. Empirical results across seven benchmarks show up to a 6.0% reduction in MSE over state-of-the-art models and robust performance across high-channel, high-sampling-rate, and ultra-long horizons. The combination of multi-scale decomposition, adaptive masking, and spectral inversion offers a practical and scalable solution for real-world LTSF tasks with diverse dynamics.

Abstract

Long-term Time Series Forecasting (LTSF) is critical for numerous real-world applications, such as electricity consumption planning, financial forecasting, and disease propagation analysis. LTSF requires capturing long-range dependencies between inputs and outputs, which poses significant challenges due to complex temporal dynamics and high computational demands. While linear models reduce model complexity by employing frequency domain decomposition, current approaches often assume stationarity and filter out high-frequency components that may contain crucial short-term fluctuations. In this paper, we introduce MMFNet, a novel model designed to enhance long-term multivariate forecasting by leveraging a multi-scale masked frequency decomposition approach. MMFNet captures fine, intermediate, and coarse-grained temporal patterns by converting time series into frequency segments at varying scales while employing a learnable mask to filter out irrelevant components adaptively. Extensive experimentation with benchmark datasets shows that MMFNet not only addresses the limitations of the existing methods but also consistently achieves good performance. Specifically, MMFNet achieves up to 6.0% reductions in the Mean Squared Error (MSE) compared to state-of-the-art models designed for multivariate forecasting tasks.

MMFNet: Multi-Scale Frequency Masking Neural Network for Multivariate Time Series Forecasting

TL;DR

MMFNet tackles long-term multivariate time series forecasting by introducing a Multi-scale Masked Frequency Transformation (MMFT) that decomposes sequences at fine, intermediate, and coarse scales, applies learnable masks in the frequency domain, and reconstructs forecasts via spectral inversion. The approach directly addresses non-stationarity and local temporal variations while maintaining computational efficiency through frequency-domain operations. Empirical results across seven benchmarks show up to a 6.0% reduction in MSE over state-of-the-art models and robust performance across high-channel, high-sampling-rate, and ultra-long horizons. The combination of multi-scale decomposition, adaptive masking, and spectral inversion offers a practical and scalable solution for real-world LTSF tasks with diverse dynamics.

Abstract

Long-term Time Series Forecasting (LTSF) is critical for numerous real-world applications, such as electricity consumption planning, financial forecasting, and disease propagation analysis. LTSF requires capturing long-range dependencies between inputs and outputs, which poses significant challenges due to complex temporal dynamics and high computational demands. While linear models reduce model complexity by employing frequency domain decomposition, current approaches often assume stationarity and filter out high-frequency components that may contain crucial short-term fluctuations. In this paper, we introduce MMFNet, a novel model designed to enhance long-term multivariate forecasting by leveraging a multi-scale masked frequency decomposition approach. MMFNet captures fine, intermediate, and coarse-grained temporal patterns by converting time series into frequency segments at varying scales while employing a learnable mask to filter out irrelevant components adaptively. Extensive experimentation with benchmark datasets shows that MMFNet not only addresses the limitations of the existing methods but also consistently achieves good performance. Specifically, MMFNet achieves up to 6.0% reductions in the Mean Squared Error (MSE) compared to state-of-the-art models designed for multivariate forecasting tasks.
Paper Structure (39 sections, 8 equations, 9 figures, 5 tables, 1 algorithm)

This paper contains 39 sections, 8 equations, 9 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Long-term Time Series Forecasting.
  4. Single-Scale Frequency Transformation (SFT).
  5. Method
  6. Overview
  7. Multi-scale Frequency Decomposition
  8. Fragmentation.
  9. Decomposition.
  10. Masked Frequency Interpolation
  11. Masking.
  12. Interpolation.
  13. Spectral Inversion
  14. Experiment
  15. Experimental Setup
  16. ...and 24 more sections

Figures (9)

  • Figure 1: MMFNet Architecture. MMFNet consists of the following key components: ① The input time series is first normalized to have zero mean using Reversible Instance-wise Normalization (RIN) lai2021revisiting. The multi-scale frequency decomposition process then divides the time series instance $X$ into fine, intermediate, and coarse-scale segments, which are subsequently transformed into the frequency domain via the Discrete Cosine Transform (DCT). ② A learnable mask is applied to the frequency segments, followed by a linear layer that predicts the transformed frequency components. ③ Finally, the predicted frequency segments from each scale are transformed back into the time domain, merged, and denormalized using inverse RIN (iRIN).
  • Figure : Fine-scale
  • Figure : Fine-scale
  • Figure : Fine-scale
  • Figure : Intermediate-scale
  • ...and 4 more figures