Efficient Time Series Forecasting via Hyper-Complex Models and Frequency Aggregation

Time series forecasting is a long-standing problem in statistics and machine learning. One of the key challenges is processing sequences with long-range dependencies. To that end, a recent line of work applied the short-time Fourier transform (STFT), which partitions the sequence into multiple subsequences and applies a Fourier transform to each separately. We propose the Frequency Information Aggregation (FIA)-Net, which is based on a novel complex-valued MLP architecture that aggregates adjacent window information in the frequency domain. To further increase the receptive field of the FIA-Net, we treat the set of windows as hyper-complex (HC) valued vectors and employ HC algebra to efficiently combine information from all STFT windows altogether. Using the HC-MLP backbone allows for improved handling of sequences with long-term dependence. Furthermore, due to the nature of HC operations, the HC-MLP uses up to three times fewer parameters than the equivalent standard window aggregation method. We evaluate the FIA-Net on various time-series benchmarks and show that the proposed methodologies outperform existing state of the art methods in terms of both accuracy and efficiency. Our code is publicly available onthis https URL.

@article{yakir2025_2502.19983,
  title={ Efficient Time Series Forecasting via Hyper-Complex Models and Frequency Aggregation },
  author={ Eyal Yakir and Dor Tsur and Haim Permuter },
  journal={arXiv preprint arXiv:2502.19983},
  year={ 2025 }
}