Time Series Forecasting Model Based on the Adapted Transformer Neural Network and FFT-Based Features Extraction

. 2025 Jan 23;25(3):652. doi: 10.3390/s25030652

Algorithm 1 Training proposed model with FFT features

Input : Time series data {t_{1}, t_{2}, . . ., t_{n}

}, m—window size, H—prediction horizon
1: for i = 1 to n-H-1 do
2:

Extract time window : {t_{i}, t_{i + 1}, . . ., t_{i + m - 1}

}
3:

Compute FFT features : fft_features = FFT ([t_{i}, t_{i + 1}, . . ., t_{i + m - 1}

])
4: Compute amplitude and phase:
(amplitude_feat, phase_feat) = FFT_transform(fft_features)
5: Train model:

model . train (x = (amplitude_feat, phase_feat), y = [t_{i + m}, t_{i + m + 1}, . . ., t_{i + m + H - 1}

])
6: end for