A novel class of reliability-based parallel hybridization (RPH) models for time series forecasting

Hybridization of individual models emerged as a predominant alternative for increasing accuracy in time series forecasting. The literature is abundant on providing hybrid methods aiming at improving forecasting accuracy and comprehensive pattern recognition. The principle behind all hybrid models' success is improving forecasting accuracy. One of the most widely used combination methods in line with the common objective of the hybridization concept is a parallel approach in which the forecasting model applied on the original time series and the weighted forecasts generate the final hybrid result. In parallel hybridization, the key is how to select the weights of each model. The weighting algorithm plays a significant role and the degree of accuracy in such models directly depends on it. However, the traditional parallel hybrid models developed to enhance forecasting accuracy employing multiple individual models simultaneously, faced some limitations, e.g., missing considering the reliability and generalization criteria of developed hybrid models. From the literature, it is observed that none of the parallel hybrid modes proposed in the literature focused on the improving reliability of the hybrid model to obtain better model generalization for unseen data. Thus, the main objective of this study is to propose a novel class of hybrid models named reliability-based parallel hybridization (RPH). The main goal of RPH methodology is to improve hybrid models' reliability rather than accuracy using a new reliable-based weighting algorithm (RWA). The RWA instead of traditional accuracy-based weighting algorithms in which error measurements are minimized, the reliability of hybrid models is maximized to determine the exact optimum weights of individual models. The RWA computed the optimum weights of forecasts regarding minimizing performance changing of the hybrid model in the validation data set. The RPH model proposed two crucial concepts for the first time: (1) Bringing up reliability in hybridization procedure (2) Proposing a novel reliable-based weighting algorithm to maximize the generalization power of the hybrid model. The bi-component version of the RPH model is proposed in this paper using ARIMA and MLP models. The forecasting power of the proposed PRH constructed based on ARIMA and MLP models is verified using the benchmark data sets e.g. the closing of Standard and Poor's 500 indexes (S&P500), the closing of the Shenzhen Integrated Index (SZII), and the opening of the Dow Jones Industrial Average Index (DJIAI). The experimental results indicate that the forecasting performance of the RPH model is much better than traditional accuracy-based parallel hybrid models.