Residual analysis using Fourier series transform in Fuzzy time series model

In this paper, we propose a new residual analysis method using Fourier series transform into fuzzy time series model for improving the forecasting performance. This hybrid model takes advantage of the high predictable power of fuzzy time series model and Fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency terms, and then have well forecasting performance. Two numerical examples are given to show that our proposed model can be applied with the best forecasting performance than the other models.