Series Hybridization of Parallel (SHOP) models for time series forecasting

Accurate forecasting of real-world systems becomes a highly challenging task due to the inherent complexity of time series modeling. Hybrid models have been successfully applied to deal with such problems and yield desired forecasting accuracy. The fundamental objective of hybridization is to exploit the unit modeling benefits of every single model and lift its disadvantages. For reaching these goals, individual models are combined in two main parallel and series frameworks. The parallel hybridization method relied on employing different individual models and integrated the weighted forecasts to capture the advantages contained in all models, concurrently. However, existing parallel hybrid models suffer from some crucial shortcomings that need to be addressed and eliminated. One of the critical deficiencies of parallel models is that the residual obtained by different models is not modeled, and the unprocessed patterns have remained in the data. The principal goal of this paper is to alleviate this deficiency of parallel hybrid models using the capability of the series hybridization strategy in modeling remaining patterns in residuals. Thus, the key innovation of this study is to combine parallel hybrid models employing a series hybridization scheme to yield an enhanced forecasting model and overcome the drawback of the parallel models. Despite the vast hybrid models proposed for combining individual models, this paper aims to combine both the above-mentioned hybrid structures instead of individual models. For this purpose, the novel hybrid model named Series Hybridization of Parallel (SHOP) model is proposed, which integrates a parallel hybrid model by series hybridization approach. In this research, Autoregressive Integrated Moving Average (ARIMA) and Multilayer perceptrons (MLP) models are used to implement the proposed hybrid SHOP structure. In this way, the SHOP contains a series hybridization of parallel hybridization of ARIMA and MLP models. The effectiveness of the SHOP model is verified by applying it to four benchmark data sets, including the closing of the DAX index, the closing of the Nikkei 225 index (N225), the opening of the Dow Jones Industrial Average Index (DJIAI), and the wind speed data in Colorado State. The predictive power of the SHOP model is evaluated by comparing the obtained results with ARIMA, MLP, LSTM, RBFNN, SVM, and traditional series and parallel hybridization of ARIMA and MLP models. Remarkably, the obtained forecasting accuracy from the SHOP model is outstanding than other models.