Fractional Fourier Transform in Time Series Prediction

Our paper where we introduce the fractional Fourier transform (FrFT) to the machine learning domain for time series analysis is now out at IEEE Signal Processing Letters!

At the intersection of classical signal processing and machine learning, AykutKocLab’s significant contribution introduced the FrFT to the time series prediction problem, which is new to FrFT’s classical application areas. The proposed method combines FrFT with Recurrent Neural Networks (RNNs) for the time series prediction problem with the motivation of utilizing a generalized transform capable of implementing infinitely many transformations to increase model performance.

We show that FrFT-based RNN models give better prediction performances than those based on either time and frequency domain by utilizing the parametric nature of FrFT that provides us to reach and select from infinitely many signal domains to represent time-series signals for better prediction.





Several signal processing tools are integrated into machine learning models for performance and computational cost improvements. Fourier transform (FT) and its variants, which are powerful tools for spectral analysis, are employed in the prediction of univariate time series by converting them to sequences in the spectral domain to be processed further by recurrent neural networks (RNNs). This approach increases the prediction performance and reduces training time compared to conventional methods. In this letter, we introduce fractional Fourier transform (FrFT) to time series prediction by RNNs. As a parametric transformation, FrFT allows us to seek and select better-performing transformation domains by providing access to a continuum of domains between time and frequency. This flexibility yields significant improvements in the prediction power of the underlying models without sacrificing computational efficiency. We evaluated our FrFT-based time series prediction approach on synthetic and real-world datasets. Our results show that FrFT gives rise to performance improvements over ordinary FT.