[pt] Quando há mudanças no padrão sazonal de uma série temporal, ao longo do tempo, fica caracterizada a presença de sazonalidade móvel. Existem evidências de séries macroeconômicas que apresentam um grau considerável de sazonalidade móvel. Atualmente, para a realização do ajuste sazonal, o programa utilizado pelo IBGE é o X-12-ARIMA, que implementa o método X-11 de ajuste sazonal. O X-11 é um dos métodos mais utilizados no mundo pelos órgãos oficiais de estatística, no entanto, quando existe sazonalidade móvel, ele não consegue tratá-la de forma adequada. Este trabalho propõe dois projetos de filtros de extração da componente sazonal, no domínio da frequência, que são adequados tanto para séries com sazonalidade estável quanto para aquelas que apresentam sazonalidade móvel. O primeiro projeto de filtros, intitulado de filtro sazonal-WLS, utiliza critérios baseados em mínimos quadrados. O desempenho do filtro sazonal-WLS é avaliado com base em sinais sazonais artificiais, para séries mensais e trimestrais, baseados nas características das séries macroeconômicas. Os resultados são comparados com o método X-11 e são identificadas as situações nas quais ele é superior ao X-11. Considerando que o filtro sazonal-WLS é tanto superior ao X-11 quanto maior for a razão entre a variação da sazonalidade e a intensidade da componente irregular, foi desenvolvido o projeto de um segundo filtro. Este novo filtro combina a abordagem de mínimos quadrados ponderados com as características dos filtros de Chebyshev, minimizando simultaneamente o erro na estimativa da sazonalidade e a influência da componente irregular. A ele intitulou-se filtro sazonal-WLS-Chebyshev. Os resultados do filtro sazonal-WLS-Chebyshev são comparados com o filtro sazonal-WLS onde observam-se algumas melhorias. / [en] A time series is said to have moving seasonality when there are changes in the seasonal pattern. There is evidence that macroeconomic series show moving seasonality. Currently, to perform a seasonal adjustment, IBGE uses the program X-12-ARIMA, which implements the seasonal adjustment method X-11. This method is worldwide adopted by official statistical agencies. However, when a time series shows changing seasonal patterns, the X-11 seasonal adjustment method generates unreliable estimates. This thesis proposes two designs of filters to extract seasonal components in the frequency domain, that are suitable for series with stable seasonality and for those with moving seasonality. The first filter, named WLS-seasonal filter, uses criteria based on least squares. The performance of this filter is assessed based on artificial seasonal series for monthly and quarterly data, based on the characteristics of real macroeconomic series. The results are compared with the ones of X-11 method, and the situations in which this filter is superior to X-11 are identified. Taking into account the fact that the performance of the WLS-seasonal filter improves in relation to the one of X-11 the higher the ratio between the variation of seasonality and irregular intensity, the design of a second filter was developed. This new filter combines the approach of weighted least squares with the Chebyshev filters characteristics, simultaneously minimizing the error in estimating the seasonal component and the influence of the irregular component. It was named WLS-Chebyshev-seasonal filter. The performance of this new filter is compared with the one of the WLS-seasonal filter, and some improvements are observed.

Singular Spectrum Analysis (SSA) is a method for decomposing and forecasting time series that recently has had major developments but it is not yet routinely included in introductory time series courses. An international conference on the topic was held in Beijing in 2012. The basic SSA method decomposes a time series into trend, seasonal component and noise. However there are other more advanced extensions and applications of the method such as change-point detection or the treatment of multivariate time series. The purpose of this work is to understand the basic SSA method through its application to the monthly average sea temperature in a point of the coast of South America, near where “EI Ni˜no” phenomenon originates, and to artificial time series simulated using harmonic functions. The output of the basic SSA method is then compared with that of other decomposition methods such as classic seasonal decomposition, X-11 decomposition using moving averages and seasonal decomposition by Loess (STL) that are included in some time series courses.

Classical time series analysis has well known methods for the study of seasonality. A more recent method of functional data analysis has proposed phase-plane plots for the representation of each year of a time series. However, the study of seasonality within functional data analysis has not been explored extensively. Time series analysis is first introduced, followed by phase-plane plot analysis, and then compared by looking at the insight that both methods offer particularly with respect to the seasonal behavior of a variable. Also, the possible combination of both approaches is explored, specifically with the analysis of the phase-plane plots. The methods are applied to data observations measuring water flow in cubic feet per second collected monthly in Newport, TN from the French Broad River. Simulated data corresponding to typical time series cases are then used for comparison and further exploration.