Estudo empírico de métodos de estimação robusta de modelos PAR e aplicação a dados de poluição do ar

Abstract

Studies about air pollution typically involve measurements and analysis of pollutants, such as PM10 (particulate matter with diameter lower than 10 µm), SO2 (sulfur dioxide) and others. These data typically have important features like serial correlation, seasonality, periodicity and the presence of peaks that despite not being atypical observations (outliers) because of their high frequency of occurrence, can be modeled as such owing to the effect that they have on the series. All these features demand special attention during data analysis. With this motivation, this study compared the performance of the robust estimator of periodic autoregressive (PAR) models proposed by Sarnaglia, Reisen & L´evyLeduc (2010) (Robust Yule-Walker) and Shao (2008) (Robust Least Squares), through a Monte Carlo study under different scenarios, including: additive outliers contamination and departures from normality. For comparison purposes, we have also considered the classical periodic Yule-Walker methodology which can be seen in McLeod (1994), for example. The practical purpose in air pollution is to evaluate if both robust methodologies are more efficient in capturing the correlation structure than the classic one. This can be checked, for instance, by the order of the autoregressive models obtained by each estimation procedure. These three methods were applied to adjust a PAR model to MP10 data of Enseada do Suá station of the air quality monitoring network of the Greater Vitória Region - ES.