Obust methods in multivariate time series

Página do item simplificado
dc.contributor.advisor1Reisen, Valderio Anselmo
dc.contributor.advisor1IDhttps://orcid.org/0000-0002-8313-7648
dc.contributor.advisor1Latteshttp://lattes.cnpq.br/9401938646002189
dc.contributor.authorCotta, Higor Henrique Aranda
dc.contributor.authorIDhttps://orcid.org/0000000203222317
dc.contributor.authorLatteshttp://lattes.cnpq.br/2488791027245465
dc.contributor.referee1Franco, Glaura da Conceicao
dc.contributor.referee1IDhttps://orcid.org/0000-0002-7994-8448
dc.contributor.referee1Latteshttp://lattes.cnpq.br/0913222654204695
dc.contributor.referee2Junior, Neyval Costa Reis
dc.contributor.referee2IDhttps://orcid.org/0000000261594063
dc.contributor.referee2Latteshttp://lattes.cnpq.br/4944106074149720
dc.contributor.referee3Albuquerque, Taciana Toledo de Almeida
dc.contributor.referee3IDhttps://orcid.org/0000-0002-6611-0283
dc.contributor.referee3Latteshttp://lattes.cnpq.br/1339985577872129
dc.contributor.referee4Palma, Wilfredo
dc.contributor.referee5Bondon, Pascal
dc.contributor.referee6Ispány, Marton
dc.contributor.referee7Renaux, Alexandre
dc.date.accessioned2024-05-30T00:48:39Z
dc.date.available2024-05-30T00:48:39Z
dc.date.issued2019-08-22
dc.description.abstractThis manuscript proposes new robust estimation me thods for the autocovariance and autocorrelation ma trices functions of stationary multivariates time se ries that may have random additives outliers. These functions play an important role in the identification and estimation of time series model parameters. Ran dom additive outliers can impact the level of one or more components of the multivariate vector. This in creases the overall variability of the series, which has an impact on the periodogram matrix and leads to a decrease in the values of the autocorrelation ma trix function. We first propose new estimators of the autocovariance and of autocorrelation matrices func tions constructed using a spectral approach conside ring the periodogram matrix periodogram which is the natural estimator of the spectral density matrix. As in the case of the classic autocovariance and autocor relation matrices functions estimators, these estima tors are affected by aberrant observations. Thus, any identification or estimation procedure using them is di rectly affected, which leads to erroneous conclusions. To mitigate this problem, we propose the use of robust statistical techniques to create estimators resistant to aberrant random observations. As a first step, we propose new estimators of auto covariance and autocorrelation functions of univariate time series. The time and frequency domains are lin ked by the relationship between the autocovariance function and the spectral density. As the periodogram is sensitive to aberrant data, we get a robust esti mator by replacing it with the M-periodogram. The M-periodogram is obtained by replacing the Fourier coefficients related to periodogram calculated by the standard least squares regression with the ones cal culated by the M-robust regression. The asymptotic properties of estimators are established. Their perfor mances are studied by means of numerical simula tions for different sample sizes and different scena rios of contamination. The empirical results indicate that the proposed methods provide close values of those obtained by the classical autocorrelation func tion when the data is not contaminated and it is re sistant to different contamination scenarios. Thus, th estimators proposed in this thesis are alternative me thods that can be used for time series with or without outliers. The estimators obtained for univariate time series are then extended to the case of multivariate series. This extension is simplified by the fact that the calculation of the cross-periodogram only involves the Fourier co efficients of each component from the univariate se ries. Again, the duality relationship between time and frequency domains is considered via the link between the autocovariance matrix function and the spectral density matrix stationary multivariate time series. The M-periodogram matrix is a robust periodogram matrix alternative to build robust estimators of the autoco variance and autocorrelation matrices functions. The asymptotic properties are studied and numerical ex periments are performed. As an example of an appli cation with real data, we use the proposed functions to adjust an autoregressive model by the Yule-Walker method to Pollution data collected in the Vit´ oria re gion Brazil (particles smaller than 10 micrometers in diameter, PM10). Finally, the robust estimation of the number of fac tors in large factorial models is considered in order to reduce the dimensionality. It is well known that the values random additive outliers affect the covariance and correlation matrices and the techniques that de pend on the calculation of their eigenvalues and ei genvectors, such as the analysis principal compo nents and the factor analysis, are affected. Thus, in the presence of outliers, the information criteria pro posed by Bai & Ng (2002) tend to overestimate the number of factors. To alleviate this problem, we pro poseto replace the standard covariance matrix with the robust covariance matrix proposed in this manus cript. Our Monte Carlo simulations show that, in the absence of contamination, the standard and robust methods are equivalent. In the presence of outliers, the number of estimated factors increases with the non-robust methods while it remains the same using robust methods. As an application with real data, we study pollutant concentrations PM10 measured in the ˆ Ile-de-France region of France.
dc.description.resumo
dc.description.sponsorshipFundação Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.formatText
dc.identifier.urihttp://repositorio.ufes.br/handle/10/13817
dc.languagepor
dc.publisherUniversidade Federal do Espírito Santo
dc.publisher.countryBR
dc.publisher.courseDoutorado em Engenharia Ambiental
dc.publisher.departmentCentro Tecnológico
dc.publisher.initialsUFES
dc.publisher.programPrograma de Pós-Graduação em Engenharia Ambiental
dc.rightsopen access
dc.subject Séries temporais multivariadas
dc.subjectRobustez
dc.subjectObservações discrepantes
dc.subjectDomínio do tempo
dc.subjectDomínio da frequência
dc.subjectMultivariate time series
dc.subjectRobustness
dc.subjectOutliers
dc.subjectTime domain
dc.subjectFrequency domain
dc.subject.br-rjbnsubject.br-rjbn
dc.subject.cnpqEngenharia Sanitária
dc.titleObust methods in multivariate time series
dc.title.alternativetitle.alternative
dc.typedoctoralThesis
Arquivos
Pacote Original
Agora exibindo 1 - 1 de 1
Imagem de Miniatura
Nome:
UFESFINALTheseHigor0809.pdf
Tamanho:
6.08 MB
Formato:
Adobe Portable Document Format
Descrição:
Baixar
Coleções
Doutorado em Engenharia Ambiental