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

Fragmented Fourier Matrix (FragFM) is a temporal-domain model for long-term time series forecasting that embeds spectral structure into the decomposition process for denoising time series. Traditional time-domain models often struggle to disentangle residual noise from seasonal components, while frequency-domain methods require complex-valued operations. FragFM bridges this gap by combining simple trend extraction with learnable symmetric Fourier-based seasonal extractors, all within the real domain. This enables effective multi-scale denoising and forecasting with minimal parameter overhead. In univariate benchmarks, SFFT achieves accuracy on par with leading frequency-based models while maintaining the efficiency and simplicity of time-domain methods.

Overview

It decomposes time series into:

• Seasonal components modeled via learned symmetric circulant matrices in the Fourier domain (efficient, interpretable harmonic components).
• Trend components extracted via moving average.
• Residual noise removed by an iterative multi-block architecture.

The model can then perform direct forecasting of future values from the denoised representation via either:

• a standard Linear layer, or
• a Low-Rank Linear layer.

SFFT is among the few temporal domain models that utilizes benefits of spectral domain yet being temporal, and achieves competitive performance on a variety of time series benchmarks.

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Key Features

✅ Fourier-based symmetric seasonal decomposition
✅ Trend extraction via moving average
✅ Stackable Decompose blocks for progressive denoising
✅ Optional Low-Rank prediction head
✅ Channel-wise or shared model architecture
✅ Lightweight, interpretable, no recurrence or self-attention

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Usage

Initialization

model = Model(configs)

Configuration Options

Parameter	Description	Default
seq_len	Input sequence length	-
pred_len	Output prediction length	-
enc_in	Number of input features	-
individual	If True, applies a separate layer per feature	False
bias	Enables bias in the low-rank layer	True
decomposer_depth	Number of stacked Decompose blocks	1
kernel_size	Moving average kernel size for Trend extraction	50
seasons	Number of Seasonal modules per Decompose block	1
enable_lowrank	Enables Low Rank or Standard Linear Layer	True
rank	Rank of the low-rank layer	30

Forward Pass

output = model(X)

Results

Acknowledgement

The listed github repositories have been used for code bases, datasets and comparisons.

• https://github.com/zhouhaoyi/Informer2020
• https://github.com/lss-1138/SparseTSF
• https://github.com/cure-lab/LTSF-Linear
• https://github.com/aikunyi/FreTS
• https://github.com/luodhhh/ModernTCN
• https://github.com/yuqinie98/patchtst
• https://github.com/thuml/iTransformer
• https://github.com/SiriZhang45/FRNet

License

This project is licensed under the MIT License.