A Hybrid Modeling Method Based on Linear AR and Nonlinear DBN-AR Model for Time Series Forecasting

Improving time series forecasting accuracy is an important work for decision makers. A single model applied on a data series may not obtain satisfactory prediction accuracy. Both theoretical and empirical findings have indicated that integration of linear model and nonlinear model may provide more accurate prediction than an individual linear or nonlinear model. This paper presents a hybrid modeling approach that combines a linear autoregressive (AR) model and a nonlinear deep belief network-based autoregressive (DBN-AR) model for time series forecasting. The proposed modeling approach first applies an AR model to fit time series data, and the error between the original date and the AR model forecast data as a nonlinear component is considered, and then the error is modeled by a DBN-AR model. DBaN-AR model is a modeling method for nonlinear time series, which uses a set of deep belief networks to approximate the state-dependent functional coefficients of state dependent auto-regressive model. The proposed hybrid model can overcome limitation of an individual model and obtain more general and more accurate forecasting result than some existing hybrid models. The experiment results demonstrate that the MSE of modeling residuals using the proposed hybrid model is largely reduced compared with the results of some single prediction models and some hybrid models for one-step-ahead and multistep-ahead forecast.