An intelligent hybridization of ARIMA with machine learning models for time series forecasting

The development of accurate forecasting systems can be challenging in real-world applications. The modeling of real-world time series is a particularly difficult task because they are generally composed of linear and nonlinear patterns that are combined in some form. Several hybrid systems that combine linear and nonlinear techniques have obtained relevant results in terms of accuracy in comparison with single models. However, the best combination function of the forecasting of the linear and nonlinear patterns is unknown, which makes this modeling an open question. This work proposes a hybrid system that searches for a suitable function to combine the forecasts of linear and nonlinear models. Thus, the proposed system performs: (i) linear modeling of the time series; (ii) nonlinear modeling of the error series; and (iii) a data-driven combination that searches for: (iii.a) the most suitable function, between linear and nonlinear formalisms, and (iii.b) the number of forecasts of models (i) and (ii) that maximizes the performance of the combination. Two versions of the hybrid system are evaluated. In both versions, the ARIMA model is used in step (i) and two nonlinear intelligent models – Multi-Layer Perceptron (MLP) and Support Vector Regression (SVR) – are used in steps (ii) and (iii), alternately. Experimental simulations with six real-world complex time series that are well-known in the literature are evaluated using a set of popular performance metrics. Our results show that the proposed hybrid system attains superior performance when compared with single and hybrid models in the literature.