Bootstrap Local para Séries Estacionárias Incompletas na Presença de Observações Atípicas: Uma Aplicação a Problemas na Área da Qualidade do Ar
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Data
2022-09-23
Autores
Solci, Carlo Correa
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Universidade Federal do Espírito Santo
Resumo
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, missing observations 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 and complicate the obtainment of confidence intervals for the parameters of stationary time series models through asymptotic theory. With this motivation, this study proposed bootstrap methodologies in the frequency domain for weakly stationary time series in the presence of missing observations and/or of contamination by additive outliers. The suggested methodologies are based on the local bootstrap of Paparoditis & Politis (1999), with the robustness being achieved by the substitution of the classical periodogram with the M-periodogram of Reisen, L´evy-Leduc & Taqqu (2017) and when there is presence of missing observations the original time series is replaced by its amplitude modulated version proposed by Parzen (1963). In this context, the efficiency of the proposed bootstrap methodologies in estimating confidence intervals of parameters of models for weakly stationary time series was verified through Monte Carlo studies under different scenarios, including: additive outliers contamination and presence of missing observations. For comparison purposes, in some cases it was also considered the bootstrap methodology of Paparoditis & Politis (1999), as well as the parameter estimates without the bootstrap via the classical and robust versions of the methodologies of Whittle (1953) and of Dunsmuir & Robinson (1981). The practical purpose in air pollution is to evaluate if the confidence intervals of the parameters obtained by the robust methodologies present a reduction in the effect of left shift that the classical intervals have due to the memory loss caused by the additive outliers, in addition to the possibility of calculating these intervals without using imputation techniques to obtain a complete time series. The proposed bootstrap methodologies were applied to calculate confidence intervals of parameters of adjustment of the autoregressive (AR) model, and in some cases also of the seasonal autoregressive (SAR) model, to MP10 data of stations of the air quality monitoring network of the Greater Vitória Region - ES.
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Poluição do Ar , Análise de Séries Temporais , Análise Espectral , Bootstrap , Periodograma , Observações Faltantes , Modulação de Amplitude , Observações Atípicas , Robustez , MP10