FragFM: Fragmented Fourier Matrix for multi-seasonality extraction in Univariate Long-Term Time Series Forecasting

Abstract

Long-term time series forecasting often relies on frequency- or time-domain decomposition to capture trends and seasonalities. Frequency based methods, such as the Discrete Fourier Transform, isolate dominant periodic components and suppress noise, but they operate in the complex domain. Time-domain models apply trend–seasonality decomposition but often capture only a single seasonality entangled with residual noise. To address these limitations, we propose the \ac{FragFM}-Fragmented Fourier Matrix--a time domain framework that incorporates spectral insights through fixed Fourier fragments. FragFM removes trends via moving averages, extracts multiple seasonal components with fragmented Fourier bases, and corrects residual noise. Operating fully in the real domain, FragFM achieves forecasting accuracy comparable to leading frequency-domain models while consistently outperforming traditional time-domain approaches. Its lightweight, interpretable design offers an efficient solution for long-term forecasting, bridging time- and frequency-domain methods. The code repository is: https://github.com/K0DX-DV1NUX/FragFM