This dissertation is composed of four articles describing inference and visualization of periodic sequences. In the first article, a nonparametric method is proposed for estimating the period and values of a periodic sequence when the data are evenly spaced in time. The period is estimated by a "leave-out-one-cycle" version of cross-validation (CV) and complements the periodogram, a widely used tool for period estimation. The CV method is computationally simple and implicitly penalizes multiples of the smallest period, leading to a "virtually" consistent estimator. The second article is the multivariate extension, where we present a CV method of estimating the periods of multiple periodic sequences when data are observed at evenly spaced time points. The basic idea is to borrow information from other correlated sequences to improve estimation of the period of interest. We show that the asymptotic behavior of the bivariate CV is the same as the CV for one sequence, however, for finite samples, the better the periods of the other correlated sequences are estimated, the more substantial improvements can be obtained. The third article proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outwards ordering induced by band depth for functional data, the descriptive statistics of a functional boxplot are: the envelope of the 50 percent central region, the median curve and the maximum non-outlying envelope. In addition, outliers can be detected by the 1.5 times the 50 percent central region empirical rule. The last article proposes a simulation-based method to adjust functional boxplots for correlations when visualizing functional and spatio-temporal data, as well as detecting outliers. We start by investigating the relationship between the spatiotemporal dependence and the 1.5 times the 50 percent central region empirical outlier detection rule. Then, we propose to simulate observations without outliers based on a robust estimator of the covariance function of the data. We select the constant factor in the functional boxplot to control the probability of correctly detecting no outliers. Finally, we apply the selected factor to the functional boxplot of the original data.

Space – time data modeling problem is analysed. Often spatial data sets are relatively small, and the points, where observations are taken, are located irregularly. When solving spatial task, usually we are interpolating or estimating the spatial average. Time series data usually are used to predict future values. Meanwhile, the space - time tasks combines both types of tasks. Few original modeling methods of spatial time series are proposed. The proposed methods firstly analyzes the univariate time series, and after removing temporal dependence, spatial dependence in the time series of residuals is measured. Aim of this dissertational work - to create time series model at new unobserved location by incorporating spatial interaction thru spatial interpolation of estimated time series parameters. Such a model is based on the spatial interpolation of time series parameters. / Disertaciniame darbe nagrinėjama erdvės – laiko duomenų modeliavimo problema. Dažnai erdvinių duomenų rinkiniai yra gana nedideli, o taškai, kuriuose pasklidę stebėjimai, išsidėstę netaisyklingai. Sprendžiant „erdvinį“ uždavinį, paprastai siekiama inerpoliuoti arba įvertinti erdvinį vidurkį. Laiko eilučių duomenys dažniausiai naudojami ateities reikšmėms prognozuoti. Tuo tarpu erdvės – laiko uždaviniai jungia abu uždavinių tipus. Pasiūlyta keletas originalių erdvinių laiko eilučių modeliavimo metodų. Siūlomi metodai pirmiausia analizuoja vienmates laiko eilutes, o pašalinus laikinę priklausomybė jose, laiko eilučių liekanoms vertinama erdvinė priklausomybė. Tikslas – sudaryti modelį, leidžiantį prognozuoti požymio reikšmę naujame, nestebėtame taške, nauju laiko momentu. Tokio modelio sudarymas remiasi laiko eilučių parametrų erdviniu interpoliavimu.

Submitted by ADRIANO MARTINS JUNQUEIRA null (adriano@geopx.com.br) on 2017-03-11T20:17:10Z No. of bitstreams: 1 Mestrado - Adriano Martins Junqueira - 2017.pdf: 8109678 bytes, checksum: d1e6cf6e83e8eac0c87d3eb5b494f810 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2017-03-16T20:19:44Z (GMT) No. of bitstreams: 1 junqueira_am_me_guara.pdf: 8109678 bytes, checksum: d1e6cf6e83e8eac0c87d3eb5b494f810 (MD5) / Made available in DSpace on 2017-03-16T20:19:44Z (GMT). No. of bitstreams: 1 junqueira_am_me_guara.pdf: 8109678 bytes, checksum: d1e6cf6e83e8eac0c87d3eb5b494f810 (MD5) Previous issue date: 2017-01-18 / A maioria dos empreendimentos do setor elétrico brasileiro não apresentam uma avaliação sistemática espaço-temporal de suas estruturas para identificar vulnerabilidades ambientais nos empreendimentos. Assim, este estudo teve como objetivo analisar a susceptibilidade de movimento de massa em linhas de transmissão, na região da Serra da Mantiqueira, sujeitas aos efeitos de chuvas tropicais e operacionalizar uma plataforma dinâmica de análise e alerta nas áreas de maior criticidade. Para este trabalho, foram levantados dados estáticos e dinâmicos na região a partir de fontes de acesso público e privado. A seguir, foram definidos os múltiplos critérios através do processo de análise hierárquica (AHP). Utilizando Sistemas de Informações Geográficas (SIG) e álgebra de mapas, foi possível determinar o mapa de susceptibilidade em cinco classes e operacionalizar a plataforma de monitoramento, análise e alerta a riscos ambientais baseando-se nas áreas identificadas e nos dados dinâmicos meteorológicos e hidrológicos. Como resultado, foi gerado um banco de dados geográfico com abrangência regional (14.000 km²), que envolveu 7 critérios: declividade, distância das linhas de transmissão, densidade de drenagem, uso do solo, tipo do solo, densidade de fraturas e falhas, e precipitação. A distribuição das classes de susceptibilidade encontradas na região de estudo foram: muito baixa (1,5%), baixa (12%), média (34,9%), alta (45,3%) e muito alta (6,2%). Foi possível ainda, identificar diferentes movimentos de massa em áreas próximas à linhas de transmissão, quanto próximas aos outros elementos de risco, como moradias, estradas, bordas de reservatórios e torres de telecomunicações. A plataforma de monitoramento operacionalizada possibilitou o estabelecimento de análises dinâmicas sobre a ocorrência de eventos naturais extremos, através do envio de notificações e acesso WEB com o mapa das áreas afetadas. Assim, este estudo pode se tornar um instrumento de avaliação, acompanhamento e gerenciamento para a gestão pública e agências reguladoras do setor elétrico. / Most of the Brazilian electric sector enterprises do not present a systematic space-time evaluation of their structures to identify environmental vulnerabilities in the projects. Thus, this study aimed to analyze the susceptibility of mass movement in transmission lines, in the Serra da Mantiqueira region, subject to the effects of tropical rains and to operationalize a dynamic platform of analysis and alertness in the most critical areas. For this work, static and dynamic data were collected in the region from public and private sources. Next, the multiple criteria were defined through the hierarchical analysis process (AHP). Using Geographic Information Systems (GIS) and map algebra, it was possible to determine the susceptibility map in five classes and to operationalize the monitoring platform for monitoring, analysis and alert to environmental risks based on identified areas and dynamic meteorological and hydrological data. As a result, a geographic database with a regional coverage (14.000 km²) was generated, involving 7 criteria: slope, distance of transmission lines, drainage density, soil use, soil type, fracture and failure density, and precipitation. The distribution of susceptibility classes found in the study region were very low (1.5%), low (12%), average (34.9%), high (45.3%) and very high (6, 2%). It was also possible to identify different mass movements in areas close to the transmission lines, as well as to other risk elements such as dwellings, roads, reservoir borders and telecommunications towers. The operationalized monitoring platform allowed the establishment of dynamic analyzes on the occurrence of extreme natural events, by sending notifications and WEB access with the map of the affected areas. Thus, this study can become an instrument of evaluation, monitoring and management for the public management and regulatory agencies of the electric sector.