Theoretical Comparison of Wavelet Transform and Fourier Transform in SARIMA-GANN Forecasting Model

Abstract

Seasonal Autoregressive Integrated Moving Average (SARIMA) model which combine seasonal differencing with an ARIMA model are used when the time series data exhibits periodic characteristics. It is popular in modelling and forecasting demand as its ability in identifying the patterns and seasonality of the series and grasping the linear trend of the series effectively. However, the assumption of linearity in many time series events may not be satisfied in practice and thus the accuracy needs to be improved. Besides, it is unable to extract the non-linearity of the series. Genetic Algorithm based Neural Network (GANN) is proposed to combine with SARIMA to overcome its shortcomings but it might occur the overfitting event. Therefore, it is important to reduce the complexity of the input data of the neural network overhead to overcome this problem. This paper contains the section of explanation of both Wavelet Transform (WT) and Fourier Transform (FT) and the discussion of the comparative pros and cons among each other in analysing signals especially in handling the overfitting problem by neural network.