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|a Time series forecasting is an active research area that has drawn most attention for applications in various fields such as engineering, finance, economic, and science. Despite the numerous time series models available, the research to improve the effectiveness of forecasting models especially for time series forecasting accuracy still continues. Several research of commonly used time series forecasting models had concluded that hybrid forecasts from more than one model often led to improved performance. Recently, one sub-model of neural network, the Group Method of Data Handling (GMDH) and several hybrid models based on GMDH method have been proposed for time series forecasting. They have been successfully applied in diverse applications such as data mining and knowledge discovery, forecasting and systems modeling, optimization and pattern recognition. However, to produce accurate results, these hybrid models require more complex network generating architecture. In addition, several types and parameters of transfer function must be predetermined and modified. Thus, in this study, two enhancements of GMDH models were proposed to alleviate the problems inherent with the GMDH algorithms. The first model was the modification of conventional GMDH method called MGMD. The second model was an enhancement of MGMDH model named HMGMDH, in order to overcome the shortcomings of MGMDH model that did not perform well in uncertainty type of data. The proposed models were then applied to forecast two real data sets (tourism demand and river flow data) and three well-known benchmarked data sets. The statistical performance measurement was utilized to evaluate the performance of the two afore-mentioned models. It was found that average accuracy of MGMDH compared to GMDH in term of R, MAE, and MSE value increased by 1.27 %, 10.96%, and 16.9%, respectively. Similarly, for HMGMDH model, the average accuracy in term of R, MAE, and MSE value also increased by 1.39%, 14.05%, 24.28%, respectively. Hence, these two models provided a simple architecture that led to more accurate results when compared to existing time-series forecasting models. The performance accuracy of these models were also compared with Auto-regressive Integrated Moving Average (ARIMA), Back-Propagation Neural Network (BPNN) and Least Square Support Vector Machine (LSSVM) models. The results of the comparison indicated that the proposed models could be considered as a useful tool and a promising new method for time series forecasting.
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