Thesis (M.S.) -- Worcester Polytechnic Institute. / Keywords: envelopes; numeric; time series; events; mining. Includes bibliographical references (leaves 71-72 ).

Alrededor de 30 años atrás, algunos estudios de tendencias a largo plazo basados en modelos numéricos, postularon que debido al aumento de la concentración de ciertos gases de efecto invernadero, se produciría un enfriamiento y encogimiento de la región F de la ionósfera (Roble, 1989). A pesar de múltiples intentos de corroborar estas predicciones, hasta ahora no hay evidencia suficiente apoyando esta conjetura. La razón para esto no es la falta de mediciones ni la estimación de tendencias, que es relativamente sencilla de efectuar, sino, la determinación correcta de las incertidumbres estadísticas en éste análisis. Para verificar esta predicción, se ha realizado un estudio de la altura de la densidad máxima de la región F utilizando los datos producidos por la ionosonda del Radio Observatorio de Jicamarca. Las mediciones se extienden desde 1993 hasta 2012. En este trabajo, primero se discutirá el criterio utilizado para armar las series de tiempo a partir de los datos obtenidos, para luego presentar el procedimiento aplicado para determinar la tendencia en el región F, que es similar al usado por Ulich (1997). Además se discutirá la precisión de este estimado, siguiendo la técnica propuesta por Weatherhead (1998), que considera posibles correlaciones en la serie de tiempo. / Tesis

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Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Ciência da Computação. / Made available in DSpace on 2012-10-20T10:06:07Z (GMT). No. of bitstreams: 1 192002.pdf: 536710 bytes, checksum: 9e40ddaa8a7c8e6259ff6b9eeaccb70c (MD5) / A solução de equações diferenciais nem sempre pode ser obtida em forma fechada. Em geral, faz-se necessário utilizar aproximações numéricas que tornem o problema solúvel computacionalmente. O método numérico escolhido na resolução do problema deve apresentar rápida convergência, consistência, estabilidade e baixo custo computacional. Dentre os métodos numéricos existentes para a resolução aproximada de equações diferenciais, consideramos os denominados métodos espectrais. Os métodos espectrais utilizam séries truncadas de funções suaves (infinitamente diferenciáveis) para representar a solução. Se o problema envolve dados suaves e condições de contorno periódicas, podemos conseguir uma rápida convergência (espectral) utilizando expansões em séries de Fourier. A convergência espectral é alcançada quando o erro de truncamento entre a série (com um número finito N de termos) e a solução exata, decai a zero mais rapidamente que qualquer potência de 1/N. As expansões espectrais para problemas não-periódicos (em domínios simples e finitos), geralmente utilizam séries em termos de polinômios de Chebyshev ou Legendre. Tais representações apresentam limitações quando precisamos resolver problemas transientes, pois o adensamento de pontos nodais próximo aos contornos implica na necessidade de pequenos passos no tempo para satisfazer a condição CFL.

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The purpose of this thesis is to develop a valid statistical procedure for the estimation of the seasonal component of an economic time series when the seasonal component is suspected to be partly additive and partly multiplicative to the trend. The proposed procedure is based on a three-way classification analysis of variance model, where the first classification is used to represent the long term trend of the series, the second classification is used to represent any regular trend or cycle within the long term trend, and the third classification is used to represent the seasonal. The interaction term between the long term trend and the seasonal may be used to represent any long term change in the nature of the seasonal. However, as the standard analysis of variance significance tests assume independently distributed residuals, it is necessary to develop a test for independence of residuals against the very likely alternative of first order (positive) serial correlation. This is done by calculating the mean and variance of the Durbin-Watson d statistic for the three-way classification analysis of variance model. A numerical example is given to illustrate the procedure. / Science, Faculty of / Mathematics, Department of / Graduate

A technique has been developed for studying surface waves on liquids. The measuring device employed Fourier analyzes the surface wave being studied. This property of the technique has been verified by three independent tests. The method developed has been applied to the study of the Rayleigh-Taylor instability of fluid surfaces. The results of this study are in good agreement with theory. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis considers an approach to evaluate the effectiveness of risk communications for prescription drugs by performing interrupted time series analysis of prescription drug volumes prior to and after the risk communication date. The paper presents methods for detecting change in the presence of autocorrelation and techniques to reduce bias in estimation. Statistical results and data plots are presented for 63 data series. Size and power of the statistical techniques are considered, and a correspondence analysis between these statistical techniques and a small group of physicians is performed. The methods considered in this thesis correspond weakly with physician sentiment, and exhibit inflated type I errors in the presence of significant autocorrelation.

This thesis examines the statistical properties of the Poisson AR(1) model of Al-Osh and Alzaid (1987) and McKenzie (1988). The analysis includes forecasting, estimation, testing for independence and specification and the addition of regressors to the model. The Poisson AR(1) model is an infinite server queue, and as such is well suited for modeling short-term disability claimants who are waiting to recover from an injury or illness. One of the goals of the thesis is to develop statistical methods for analyzing series of monthly counts of claimants collecting short-term disability benefits from the Workers' Compensation Board (WCB) of British Columbia. We consider four types of forecasts, which are the k-step ahead conditional mean, median, mode and distribution. For low count series the k-step ahead conditional distribution is practical and much more informative than the other forecasts. We consider three estimation methods: conditional least squares (CLS), generalized least squares (GLS) and maximum likelihood (ML). In the case of CLS estimation we find an analytic expression for the information and in the GLS case we find an approximation for the information. We find neat expressions for the score function and the observed Fisher information matrix. The score expressions leads to new definitions of residuals. Special care is taken to test for independence since the test is on the boundary of the parameter space. The score test is asymptotically equivalent to testing whether the CLS estimate of the correlation coefficient is zero. Further we define a Wald and likelihood ratio test. Then we use the general specification test of McCabe and Leybourne (1996) to test whether the model is sufficient to explain the variation found in the data. Next we add regressors to the model and update our earlier forecasting, estimation and testing results. We also show the model is identifiable. We conclude with a detailed application to monthly WCB claims counts. The preliminary analysis includes plots of the series, autocorrelation function and partial autocorrelation function. Model selection is based on the preliminary analysis, t-tests for the parameters, the general specification test and residuals. We also include forecasts for the first six months of 1995. / Business, Sauder School of / Graduate

Ph.D. / Harmonic time series are often used to describe the periodic nature of a time series, for example the periodic nature of a variable star’s observed light curve. Statistical methods for determining the number of harmonic components to include in harmonic time series are limited. In this thesis a stepwise bootstrap procedure based on a F-type statistic is suggested. The performance of the stepwise procedure is compared to that of Schwartz’s Bayesian Criterion (SBC) and a procedure based on a statistic described by Siegel (1980). Harmonic series with correlated noise terms and irregularly spaced observations are also considered. Tests to detect changes in harmonic parameters are also derived in this thesis. A cumulative sum statistic to test for constant amplitude is derived. It is shown that testing for constant amplitude is equivalent to testing for constant slope in simple linear regression. We also derive a likelihood ratio statistic to test for constant amplitude. It is shown that the latter likelihood ratio statistic is asymptotically equivalent to the cumulative sum statistic. These statistics are compared to a quadratic form statistic used by Koen (2009). Likelihood ratio tests are also derived for detecting changes in the frequency or phase of harmonic time series. Graphical devices to aid in diagnostic checking are suggested.