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

摘要

This paper considers the possibility that the daily average ParticulateMatter (PM$_{10}$) concentration is a seasonal fractionally integrated processwith time-dependent variance (volatility). In this context, one convenientextension is to consider the SARFIMA model (Reisen, et al, 2006a,b) with GARCHtype innovations. The model is theoretically justified and its usefulness iscorroborated with the application to PM$_{10}$ concentration in the city ofCariacica-ES (Brazil). The model adjusted was able to capture the dynamics inthe series. The out-of-sample forecast intervals were improved by consideringheteroscedastic errors and they were able to identify the periods of morevolatility.