Ciclo de seminários do Programa de Pós-Graduação em Matemática Aplicada e Estatística da UFRN - 2017

Título: PCA and Robust Factor Analysis of Time Series: Application to Air Pollution data

Palestrante: Prof. Dr. Valdério A. Reisen - DEST-CCE/PPGEA-CT - Universidade Federal do Espírito Santo.

Quando: 24 de novembro de 2017, sexta-feira, às 14:00h.
Onde: Sala H3  – Setor de aulas III.

Resumo.  This paper discusses principal component analysis (PCA) and the factor modeling for high-dimensional time series in the presence of additive outliers.  In the case of PCA, this technique is investigated under time series models with the aim to verify the correlation effect on the theoretical  and estimated eigenvalues. Some properties are discussed and the generalized additive model (GAM) is used as an application of the PCA procedure discussed. The factor model studied by Lam and Yao (2012) is extended to consider the presence of additive outliers. The estimators of the number of factors are obtained by an eigenanalysis of a non-negative definite matrix, i.e., the covariance matrix or the robust covariance matrix. The proposed methodology is analyzed in terms of the convergence rate of the number factors by means of Monte Carlo simulations. As an example of application, the robust factor analysis is utilized to identify pollution behavior for the pollutant PM10 in the Greater Vitória region (ES, Brazil) aiming to reduce the dimensionality of the data and for forecasting investigation.