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Interpretable Multivariate Time Series Forecasting Using Neural Fourier Transform

Noam Koren, Kira Radinsky

TL;DR

The paper introduces the Neural Fourier Transform (NFT), a novel approach for multivariate time series forecasting that combines a multidimensional Discrete Fourier Transform with Temporal Convolutional Networks to learn explicit seasonal components and trends. NFT incorporates a Seasonality block based on 2-DFT and a Trend Block (plus an optional Generic Block) to decompose signals into interpretable Fourier and polynomial components, trained end-to-end on multiple datasets. Empirically, NFT achieves state-of-the-art accuracy across fourteen diverse datasets, with statistically significant improvements and favorable training times, while offering interpretable representations of seasonal and trend patterns. The work suggests strong potential for real-time, interpretable forecasting in complex multivariate settings and points to future integration with Prophet-based frameworks and long-horizon forecasting.

Abstract

Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines multi-dimensional Fourier transforms with Temporal Convolutional Network layers to improve both the accuracy and interpretability of forecasts. The Neural Fourier Transform is empirically validated on fourteen diverse datasets, showing superior performance across multiple forecasting horizons and lookbacks, setting new benchmarks in the field. This work advances multivariate time series forecasting by providing a model that is both interpretable and highly predictive, making it a valuable tool for both practitioners and researchers. The code for this study is publicly available.

Interpretable Multivariate Time Series Forecasting Using Neural Fourier Transform

TL;DR

The paper introduces the Neural Fourier Transform (NFT), a novel approach for multivariate time series forecasting that combines a multidimensional Discrete Fourier Transform with Temporal Convolutional Networks to learn explicit seasonal components and trends. NFT incorporates a Seasonality block based on 2-DFT and a Trend Block (plus an optional Generic Block) to decompose signals into interpretable Fourier and polynomial components, trained end-to-end on multiple datasets. Empirically, NFT achieves state-of-the-art accuracy across fourteen diverse datasets, with statistically significant improvements and favorable training times, while offering interpretable representations of seasonal and trend patterns. The work suggests strong potential for real-time, interpretable forecasting in complex multivariate settings and points to future integration with Prophet-based frameworks and long-horizon forecasting.

Abstract

Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines multi-dimensional Fourier transforms with Temporal Convolutional Network layers to improve both the accuracy and interpretability of forecasts. The Neural Fourier Transform is empirically validated on fourteen diverse datasets, showing superior performance across multiple forecasting horizons and lookbacks, setting new benchmarks in the field. This work advances multivariate time series forecasting by providing a model that is both interpretable and highly predictive, making it a valuable tool for both practitioners and researchers. The code for this study is publicly available.
Paper Structure (20 sections, 7 equations, 4 figures, 2 tables)

This paper contains 20 sections, 7 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Interpretable Time Series Forecasting
  4. Multidimensional Fourier Transform
  5. Problem Statement
  6. Neural Fourier Transform (NFT)
  7. Learning Fourier Coefficients via TCN
  8. Expending NFT to Non-Seasonal Effects
  9. Trend Block
  10. Generic Block
  11. Model Interpretability
  12. Empirical Evaluation
  13. Experimental Methodology
  14. Datasets
  15. Baseline Models
  16. ...and 5 more sections

Figures (4)

  • Figure 1: Architecture of the Neural Fourier Transform (NFT) model. The diagram illustrates the arrangement of the Seasonality and Trend Blocks within the model, highlighting the multi-dimensional Fourier Transform and Temporal Convolutional Network layers.
  • Figure 2: MSE results across different forecasting methods and datasets
  • Figure 3: Seasonal and Trend components of forecast
  • Figure 4: MSE results of NFT and NFT with LSTM and FC layers