Name: Wanderson de Paula Pinto
Type: PhD thesis
Publication date: 22/08/2019

Namesort descending Role
Valdério Anselmo Reisen Advisor *

Examining board:

Namesort descending Role
Glaura da Conceição Franco External Examiner *
Márton Ispány External Examiner *
Neyval Costa Reis Jr. Internal Examiner *
Pascal Bondon External Examiner *
Taciana Toledo de Almeida Albuquerque Internal Examiner *
Valdério Anselmo Reisen Advisor *
Wilfredo Omar Palma Manriquez External Examiner *

Summary: 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 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 underestimation 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 Vitoria (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.

Access to document

Acesso à informação
Transparência Pública

© 2013 Universidade Federal do Espírito Santo. Todos os direitos reservados.
Av. Fernando Ferrari, 514 - Goiabeiras, Vitória - ES | CEP 29075-910