Parallel hybridization of series (PHOS) models for time series forecasting

Literature indicates that many efforts have been conducted toward the development of forecasting models with a high degree of accuracy. Combining different models is known as a powerful alternative to access more reliable and more accurate results than single models. Given the great importance of hybridization theory, various hybrid models have been proposed in the literature of time series forecasting. Series hybrid approaches are one of the most well study and the most widely used hybridization models, in which components are sequentially applied. However, according to the modeling essence of this hybrid structure, the performance of the series hybrid models is directly dependent on the order of using components and modeling sequence. Besides, selecting the best modeling order that can yield the best performance in all situations is a problematic theoretical as well as practical task. Thus, the main purpose of this paper is to eliminate the drawback of series models, regarding modeling order selection using a parallel hybridization schema, which is addressed for the first time. The core principle of the proposed parallel hybridization of series (PHOS) models is to improve the series hybrid model’s forecasting accuracy by integrating two hybrid structures in contrast to existing hybrid models, which emphasize only the combination of individual models. The proposed model decomposes the original time series into two linear and nonlinear parts and uses the autoregressive integrated moving average (ARIMA) and multilayer perceptron neural network (MLP) models to model underlying patterns, incorporating two series models including ARIMA–MLP and MLP–ARIMA. Finally, the series models are integrated as components of the parallel hybridization scheme. Moreover, an ordinary least square algorithm is developed to determine the optimal weights of these two components. Three benchmark data sets, including the closing of the DAX index, the closing of the Nikkei 225 index (N225), and the opening of the Dow Jones Industrial Average Index, are used for empirical analysis and verifying the effectiveness of the PHOS model. The empirical analysis indicates that the PHOS model can improve the forecasting performance of both series ARIMA–MLP and MLP–ARIMA models as well as individual models and some parallel hybrid models.