Aggregated moving functional median in robust prediction of hierarchical functional time series - an application to forecasting web portal 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 robustness and computational complexity. An empirical usefulness of our method is presented on example of management of a certain web portal divided into four subservices. An extensive simulation study involving hierarchical systems consisted of FAR(1) processes and Wiener processes has been conducted as well.