Forecasting of a Hierarchical Functional Time Series on Example of Macromodel for the Day and Night Air Pollution in Silesia Region — A Critical Overview

Abstract

In economics we often face a system which intrinsically imposes a structure
of hierarchy of its components, i.e., in modeling trade accounts related to
foreign exchange or in optimization of regional air protection policy. A
problem of reconciliation of forecasts obtained on different levels of hierarchy
has been addressed in the statistical and econometric literature many times and
concerns bringing together forecasts obtained independently at different levels
of hierarchy. This paper deals with this issue with regard to a hierarchical
functional time series. We present and critically discuss a state of art
and indicate opportunities of an application of these methods to a certain
environment protection problem. We critically compare the best predictor
known from the literature with our own original proposal. Within the paper
we study a macromodel describing the day and night air pollution in Silesia
region divided into five subregions.