Double Functional Median in Robust Prediction of Hierarchical Functional Time Series - An Application to Forecast Internet Service Users Behaviors

In this article, a new nonparametric and robust method of forecasting hierarchical functional time series is presented. The method is compared with Hyndman and Shang's method with respect to their unbiasedness, effectiveness, robustness, and computational complexity. Taking into account results of the analytical, simulation and empirical studies, we come to the conclusion that our proposal is superior over the proposal of Hyndman and Shang with respect to some statistical criteria and especially with respect to their robustness and computational complexity. The studied empirical example relates to the management of Internet service divided into four subservices.