Sequence in Hybridization of Statistical and Intelligent Models in Time Series Forecasting

With the importance of forecasting with a high degree of accuracy, the increasing attention has been evolved to combine individual models, especially statistical and intelligent ones. The main aim of such that hybrid models is to extract unique modeling strengths in linear and nonlinear pattern recognition, respectively. Therefore, different hybridization methods are proposed in recent literature for time series forecasting. One of the most widely-used combination strategies applied for numerous forecasting problems to yield more accurate results is the series hybrid strategy. In this hybridization methodology, components of a time series are separated and then modeled sequentially by choosing appropriate single models. However, the most accurate series hybrid model developed by determining the proper arrangement of single models. Thus, one of the critical issues in constructing series hybrid models is how to choose the appropriate sequence of individual models in a sequential modeling procedure. Although it is critically affecting on obtaining more accurate forecasting results, it has not been appropriately discussed in the literature of time series forecasting. Thus, in this paper, the performance of two possible sequence modeling procedures, including linear–nonlinear and nonlinear–linear, are evaluated. For this purpose, autoregressive integrated moving average (ARIMA), support vector machines (SVM), and multilayer perceptrons (MLP) models are chosen due to the popularity of these approaches for developing statistical/intelligent series hybrid models. Five well-known real data sets, e.g., Wolf’s Sunspot, Canadian Lynx, British pound/US dollar exchange rate, Nikkei 225 stock price, and the Colorado wind speed, are considered to distinguish better sequences. In this way, the main objective of this paper is to response this unanswered question in the literature that which sequence of single models can lead to obtain much better accuracy in constructing bi-component series hybrid models. Empirical results indicate that choosing the nonlinear intelligent model as first component in sequential modeling procedure can lead to yield more accurate results. Both SVM–ARIMA and MLP–ARIMA models can improve the performance of the ARIMA–SVM and ARIMA–MLP, respectively. Therefore, it can be concluded that the nonlinear–linear series hybrid models may produce more accurate results than linear–nonlinear hybrid models for time series forecasting.