Principal components analysis in multivariate time series with conditional heteroscedasticity and outliers: an application for air pollution in the Greater Vitória Region, Espírito Santo, Brazil

Name: Edson Zambon Monte
Type: PhD thesis
Publication date: 01/04/2016

Namesort descending Role
Valdério Anselmo Reisen Advisor *

Examining board:

Namesort descending Role
Celso Jose Munaro Internal Examiner *
Márton Ispány External Examiner *
Neyval Costa Reis Jr. Internal Examiner *
Pascal Bondon External Examiner *
Taciana de Lemos Dias Internal Examiner *
Valdério Anselmo Reisen Advisor *

Summary: Issues relating to air quality have become increasingly important, since many health problems come from air pollution. In addition, air pollution contributes to the degradation of the environment,contributing to the greenhouse effect. Thus, several studies adopting technical statistics have been conducted in order to contribute in the making of public and private actors with regard to combating pollution, prevention of high concentrations and formulation of laws for this purpose. The classical principal component analysis (PCA) is a statistical methodologies adopted. The PCA is used for dimensional reduction, cluster analysis, regression analysis, among others. However, among the studies that have adopted the classical PCA, a common feature is to neglect the conditional heteroscedasticity and/or the presence of additive outliers, which may lead to spurious results (misleading), since the estimated autocovariance matrix may be biased (estimated incorrectly). It is possible to note that the time series related to air pollution tend to present conditional heteroscedasticity and additive outliers. Then, the first paper of this thesis proposed to apply a multivariate filter VARFIMA-GARCH to the original data and use the classical PCA on residuals of the VARFIMA-GARCH model. Besides the volatility, this model was used to filter the temporal correlation and the long memory behavior. The application of the PCA on the residuals of the VARFIMA-GARCH model was more consistent with the environmental characteristics of the Greater Victoria Region (GVR), Esp´ırito Santo, Brazil, than the application using the original data The second paper, that is the core of this thesis, the technique of principal volatility components (PVC), proposed by Hu e Tsay (2014), was extended for a robust approach (RPVC), in order to capture the volatility present in the multivariate time processes, but considering the effects of additive outliers on conditional covariance, since these outliers may mask (“hide”) the conditional heteroscedasticity or even produce spurious volatility. The proposed RPVC improved the predictions of PM10 exceedance days in the Laranjeiras station, in the GVR.

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