Abstract
Hierarchical time series is a set of data sequences organized by aggregation constraints to represent many real-world applications in research and the industry. Forecasting of hierarchical time series is a challenging and time-consuming problem owing to ensuring the forecasting consistency among the hierarchy levels based on their dimensional features. The excellent empirical performance of our Deep Long Short-Term Memory (DLSTM) approach on various forecasting tasks motivated us to extend it to solve the forecasting problem through hierarchical architectures. Toward this target, we develop the DLSTM model in auto-encoder (AE) fashion and take full advantage of the hierarchical architecture for better time series forecasting. DLSTM-AE works as an alternative approach to traditional and machine learning approaches that have been used to manipulate hierarchical forecasting. However, training a DLSTM in hierarchical architectures requires updating the weight vectors for each LSTM cell, which is time-consuming and requires a large amount of data through several dimensions. Transfer learning can mitigate this problem by training first the time series at the bottom level of the hierarchy using the proposed DLSTM-AE approach. Then, we transfer the learned features to perform synchronous training for the time series of the upper levels of the hierarchy. To demonstrate the efficiency of the proposed approach, we compare its performance with existing approaches using two case studies related to the energy and tourism domains. An evaluation of all approaches was based on two criteria, namely, the forecasting accuracy and the ability to produce coherent forecasts through through the hierarchy. In both case studies, the proposed approach attained the highest accuracy results among all counterparts and produced more coherent forecasts.