An Optimal Hybrid Bi-Component Series-Parallel Structure for Time Series Forecasting

Modeling and forecasting of real-world systems have become one of the most critical needs in different science kinds. Among various factors considered in selecting an appropriate forecasting tool, accuracy is known as the most important criterion. Therefore, the most critical issue in recent forecasting studies is related to improving forecasting accuracy. These studies can be generally categorized into two categories of proposing new single models and developing hybrid models. It has been proven from both theoretical and empirical points of view that combining different models can generate superior results and improve single models' predictive performance. However, despite the popularity and the widespread use of hybrid models, some influential factors, such as the structure of hybridization, number of components, type of components, etc., affect hybrid models' performance that must be appropriately chosen by designers. It is the most challenging subject in the literature of time series forecasting in two recent decades. Several researchers examine different combinations of these factors in order to conclude which one is better. In this way, several different papers have been published in hybridization literature; however, none can prove that its proposed structure is universally better than others. Thus, this paper's primary purpose is to propose an optimal hybrid structure for time series forecasting. The proposed structure's main idea is to simultaneously use remarkable features of series and parallel structures and lift their limitations by hybridization of these two methodologies. In this way, in some parts of the modeling process, parallel structure is used, and in some other parts, the series structure is used. In this paper, a bi-component hybrid model of statistical classic and artificial intelligence models is presented as the initial implementation of the proposed methodology. Its performance is theoretically and empirically evaluated. The optimality of the proposed structure is mathematically demonstrated from the theoretical point of view. It is universally proven that the constructed hybrid model based on the proposed structure will achieve the best performance among all other hybrid models constructed based on series and parallel structures by the same conditions, e.g., number and type of components. In addition, the empirical results of ten benchmark data sets with different characteristics indicate that the profitability of the proposed structure is statistically significant.