A modified weighting system for combined forecasting methods based on the correlation coefficients of the individual forecasting models

Herein, a modified weighting for combined forecasting methods is established. These weights are used to adjust the correlation coefficient between the actual and predicted values from five individual forecasting models based on their correlation coefficient values and ranking. Time-series datasets with three patterns (stationary, trend, or both trend and seasonal) were analyzed by using the five individual forecasting models and three combined forecasting methods: simple-average, Bates-Granger, and the proposed approach. The MAPE and RMSE results indicate that the proposed method outperformed the others, especially when the time-series pattern was stationary and improved the forecasting accuracy of the worst and best individual forecasting models by 35–37% and 7–10%, respectively. Moreover, the proposed method showed improvements in MAPE and RMSE of around 18–20% and 9–11% compared to the simple-average and Bates-Granger methods, respectively. In addition, the combined forecasting methods outperformed the individual forecasting models when analyzing non-stationary data. Remarkably, the performances of the proposed and Bates-Granger methods were almost the same, with improvements in MAPE and RMSE in the range of 1–2% on average. Therefore, the proposed method for creating weights based on the correlation coefficients of the individual forecasting models greatly improves combined forecasting methods.