Modeling and forecasting daily average PM$_{10}$ concentrations by a seasonal ARFIMA model with volatility

TL;DR

This paper develops a seasonal ARFIMA model with GARCH-type volatility to accurately model and forecast daily PM$_{10}$ concentrations, capturing dynamics and volatility patterns in Cariacica-ES, Brazil.

Contribution

It introduces a theoretically justified SARFIMA-GARCH model for PM$_{10}$ forecasting, improving forecast intervals by accounting for heteroscedasticity.

Findings

Model effectively captures PM$_{10}$ dynamics.

Forecast intervals improved with heteroscedastic errors.

Identifies periods of increased volatility.

Abstract

This paper considers the possibility that the daily average Particulate Matter (PM$_{10}$) concentration is a seasonal fractionally integrated process with time-dependent variance (volatility). In this context, one convenient extension is to consider the SARFIMA model (Reisen, et al, 2006a,b) with GARCH type innovations. The model is theoretically justified and its usefulness is corroborated with the application to PM$_{10}$ concentration in the city of Cariacica-ES (Brazil). The model adjusted was able to capture the dynamics in the series. The out-of-sample forecast intervals were improved by considering heteroscedastic errors and they were able to identify the periods of more volatility.