Identifying Seasonality in Time Series by Applying Fast Fourier Transform

Abstract

The importance of studying time series is that most forecasting models assume that the time series must be stationary. In addition, non-stationary time series can cause unexpected behaviors or create a non-existing relationship between two variables. The aim of this study is to shine new light on the Fast Fourier Transform (FFT) technique through an examination of its efficiency in identifying the trend and seasonality by applying it to many time series. A comparison between the FFT technique and Autocorrelation Function (ACF) has been conducted as well. The results show that the FFT technique has acceptable performance in identifying the trend and seasonality. The most obvious observation is that, unlike the FFT technique, the ACF has limitations in determining the exact time of the seasonality that repeats itself.