A hybrid modelling method for time series forecasting based on a linear regression model and deep learning

Abstract

Time series forecasting has important theoretical significance and engineering application value. A number of studies have shown that hybrid modelling is very successful in various modelling applications, and both theoretical and empirical findings have shown that hybrid modelling is an effective method to improve the accuracy of time series models. This paper proposes a hybrid model that combines a linear regression (LR) model and deep belief network (DBN) model for the prediction of time series data. In the hybrid model, the linear AR (auto-regression) LR model or ARIMA (auto-regressive integrated moving average) model and the nonlinear DBN model are explored to capture the linear and nonlinear behaviours of a time series, respectively. We first use an LR model to fit the original data and obtain the LR model residuals between the original data and the predicted data of the LR model. Then, the residuals are regarded as the nonlinear component and are used as inputs into the DBN model. The LR model prediction and the output of the DBN model are the final forecasting value for the time series, which takes full advantage of the two models for predicting time series. The proposed hybrid model and other existing models are applied to four well-known time series for comparison, and the results show that the proposed hybrid model has a high prediction accuracy and may be a useful tool for time series forecasting.