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

TL;DR

This paper reviews methods for forecasting hierarchical functional time series, applies them to model day and night air pollution in Silesia, and compares existing predictors with a new proposed approach.

Contribution

It introduces a novel forecasting method for hierarchical functional time series and applies it to environmental pollution data, critically comparing it with existing techniques.

Findings

The proposed method outperforms existing predictors in accuracy.

Hierarchical reconciliation improves forecast consistency across levels.

Application to Silesia air pollution demonstrates practical utility.

Abstract

In economics we often face a system, which intrinsically imposes a structure of hierarchy of its components, i.e., in modelling 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 for many times and concerns bringing together forecasts obtained independently at different levels of hierarchy. This paper deals with this issue in case of 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 a day and night air pollution in Silesia region divided into five subregions.