Number of time series per hierarchical level.

This study aims to investigate whether combining forecasts generated from different models can improve forecast accuracy rather than individual models using the hierarchical time series. Various approaches of hierarchical forecasting have been considered; a bottom-up, top-down, and an optimal combination approach. Autoregressive moving averages (ARIMA) and exponential smoothing (ETS) were used as forecasting models in creating forecasting for all levels in the hierarchy to show the effect of different forecasting methods for each hierarchical model. The results indicated that the Minimum Trace Sample estimator (MinT-Sample) and the bottom-up approaches with the ARIMA model have good predictive performance than other approaches. Moreover, the forecasts from the MinT-Sample and bottom-up approaches were combined using five different combining methods. The experimental results showed that the (AC) method is superior to all other combining methods and more accurate than other individual models at level zero (international total trade in Egypt) and level one (total exports, and total imports). So, combining forecasts generated from different models by hierarchical time series leads to more accurate forecasting of the value of imports and exports which will improve the overall international trade performance, and that is through using the forecasting values of imports and exports to plan for improving the trade balance and drawing up a more efficient production policy. Finally, the study recommends using hierarchical forecasting methods in the areas of international trade, and the Ministry of Commerce and Industry could adopt the results of this study to produce precise forecasts for international trade. Moreover, the results of this study are to be a guide for the researchers to apply these approaches in other fields to improve the performance of forecasting.