An Ensemble Model of Arima and Ann with Restricted Boltzmann Machine Based on Decomposition of Discrete Wavelet Transform for Time Series Forecasting

Time series forecasting research area mainly focuses on developing effective forecasting models to improve prediction accuracy. An ensemble model composed of autoregressive integrated moving average (ARIMA), artificial neural network (ANN), restricted Boltzmann machines (RBM), and discrete wavelet transform (DWT) is presented in this paper. In the proposed model, DWT first decomposes time series into approximation and detail. Then Khashei and Bijari’s model, which is an ensemble model of ARIMA and ANN, is applied to the approximation and detail to extract their both linear and nonlinear components and fit the relationship between the components as a function instead of additive relationship. Furthermore, RBM is used to perform pre-training for generating initial weights and biases based on inputs feature for ANN. Finally, the forecasted approximation and detail are combined to obtain final forecasting. The forecasting capability of the proposed model is tested with three well-known time series: sunspot, Canadian lynx, exchange rate time series. The prediction performance is compared to the other six forecasting models. The results indicate that the proposed model gives the best performance in all three data sets and all three measures (i.e. MSE, MAE and MAPE).