A Hybrid Model of ARIMA and ANN with Discrete Wavelet Transform for Time Series Forecasting

Abstract

Improving the prediction performance is a main objective in time series forecasting research area. Wavelet transform has been used for decomposing time series into approximation and detail before further analysis with forecasting models. However, generally, the approximation and the detail are assumed as either linear or nonlinear. In fact, the wavelet transform is not for decomposing the original time series into linear and nonlinear time series. Therefore, this study proposes a hybrid forecasting model of discrete wavelet transform (DWT), autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) without linear or nonlinear assumption on the approximation and the detail. The proposed model decomposes the time series by the DWT to get the approximation and the detail. Then, the approximation and the detail are separately analyzed by Zhang’s hybrid model involving the ARIMA and the ANN in order to capture both linear and nonlinear components of the approximation and the detail. Finally, the linear and nonlinear components are combined for final forecasting. The proposed model has been tested with three well-known data sets: Wolf’s sunspot, Canadian lynx and British pound/US dollar exchange rate. The experimental results indicate that the proposed model can outperform the ARIMA, the ANN, and the Zhang’s hybrid model in all three tested time series and measures (i.e. MSE, MAE and MAPE).