Análise espectral de séries temporais de concentrações de poluentes atmosféricos com dados faltantes

• Autor(a) principal: Pinto, Wanderson de Paula
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Espírito Santo (riUfes)
• Texto Completo: http://repositorio.ufes.br/handle/10/13379
• topic: Engenharia Sanitária; Séries temporais; Análise espectral; Dados faltantes; Poluição do ar; Periodograma de Lomb-Scargle; Spectral analysis; Missing data; Air pollution; Lomb-scargle periodogram; subject.br-rjbn

Air pollution has significantly affected living beings, even when their values are below what is allowed by regulators. In this regard, air quality issues have become increasingly important as a number of health problems arise from air pollution. In this way, several studies applied time series analysis techniques have been carried out, aiming to contribute as tools in the decision making of the public and private agents with respect to the prevention of high concentrations, the control of air pollution and the formulation legislation for this purpose. One of the sta tistical methodologies adopted is the spectral analysis, which is used to identify properties of the dataset, such as seasonality. However, it is noted that among studies that have adopted this technique, a common feature is to neglect the presence of missing data, which may lead to un derestimation of the accuracy of the results. Note that in the time series related to atmospheric pollution a frequent problem is the presence of missing data, usually due to the failure of the monitoring equipment. Thus, this paper concentrates on the study of methodologies used to estimate the autocorrelation function and the spectral density of univariate time series in the presence or absence of missing data. The suggested estimators are based on the Amplitude Modulated methodology, proposed by Parzen (1963), and in the Lomb-Scargle (LOMB, 1976; SCARGLE, 1982) periodogram. In addition, we proposed estimators of autocovarianance and autocorrelation functions of time series, considering the connection between the time domain and frequency by means of the relation between the autocovariance function and the spectral density. Thus, in the first article of this thesis were presented three methods to estimate the au tocorrelation function of univariate stationary time series in the presence of missing data. The theoretical properties of the estimators were evaluated and their performances for finite sam ples investigated through a numerical simulation study. Finally, it was proposed the application of these methodologies to evaluate a time series of concentrations of PM10 of the Region of Greater Vit´ oria (RGV), Esp´ ırito Santo, Brazil, with missing data. The second article presents an estimation method for the autocorrelation and autocovariance functions of time series con sidering the connection between time domain and frequency. The asymptotic properties of the method are evaluated through a Monte Carlo simulation study for different sample sizes and percentages of missing data. In the third article, which is the main contribution of this thesis, two methods were proposed to estimate the spectral density function of stationary time series in the presence of missing data. The effect of the percentage of missing data on the employed estimators was studied. The methods were analyzed through simulations and an application to actual PM10 data monitored at the RGV was also considered. allowed by regulators. In this regard, air quality issues have become increasingly important as a number of health problems arise from air pollution. In this way, several studies applied time series analysis techniques have been carried out, aiming to contribute as tools in the decision making of the public and private agents with respect to the prevention of high concentrations, the control of air pollution and the formulation legislation for this purpose. One of the statistical methodologies adopted is the spectral analysis, which is used to identify properties of the dataset, such as seasonality. However, it is noted that among studies that have adopted this technique, a common feature is to neglect the presence of missing data, which may lead to un derestimation of the accuracy of the results. Note that in the time series related to atmospheric pollution a frequent problem is the presence of missing data, usually due to the failure of the monitoring equipment. Thus, this paper concentrates on the study of methodologies used to estimate the autocorrelation function and the spectral density of univariate time series in the presence or absence of missing data. The suggested estimators are based on the Amplitude Modulated methodology, proposed by Parzen (1963), and in the Lomb-Scargle (LOMB, 1976; SCARGLE, 1982) periodogram. In addition, we proposed estimators of autocovarianance and autocorrelation functions of time series, considering the connection between the time domain and frequency by means of the relation between the autocovariance function and the spectral density. Thus, in the first article of this thesis were presented three methods to estimate the autocorrelation function of univariate stationary time series in the presence of missing data. The theoretical properties of the estimators were evaluated and their performances for finite samples investigated through a numerical simulation study. Finally, it was proposed the application of these methodologies to evaluate a time series of concentrations of PM10 of the Region of Greater Vit´ oria (RGV), Esp´ ırito Santo, Brazil, with missing data. The second article presents an estimation method for the autocorrelation and autocovariance functions of time series considering the connection between time domain and frequency. The asymptotic properties of the method are evaluated through a Monte Carlo simulation study for different sample sizes and percentages of missing data. In the third article, which is the main contribution of this thesis, two methods were proposed to estimate the spectral density function of stationary time series in the presence of missing data. The effect of the percentage of missing data on the employed estimators was studied. The methods were analyzed through simulations and an application to actual PM10 data monitored at the RGV was also considered.