When experimental units exhibit a smooth trend over time or in space, random allocation of treatments may no longer be appropriate. Instead, systematic run orders may have to be used to reduce or eliminate the effects of such a trend. The resulting designs are referred to as trend-free designs. We consider here, in particular, linear trend-free designs for factorial treatment structures such that estimates of main effects and two-factor interactions are trend-free. In addition to trend-freeness we incorporate a general cost structure and propose methods of constructing optimal or near-optimal full or fractional factorial designs. Building upon the generalized foldover scheme (GFS) introduced by Coster and Cheng (1988) we develop a procedure of selection of foldover vectors (SFV) which is a construction method for an appropriate generator matrix. The final optimal or near-optimal design can then be developed from this generator matrix. To achieve a reduction in the amount of work, i.e., a reduction of the large number of possible generator matrices, and to make this whole process easier to use by a practitioner, we introduce the systematic selection of foldover vectors (SSFV). This method does not always produce optimal designs but in all cases practical compromise designs. The cost structure for factorial designs can be modeled according to the number of level changes for the various factors. In general, if cost needs to be kept to a minimum, factor level changes will have to be kept at a minimum. This introduces a covariance structure for the observations from such an experiment. We consider the consequences of this covariance structure with respect to the analysis of trend-free factorial designs. We formulate an appropriate underlying mixed linear model and propose an AIC-based method using simulation studies, which leads to a useful practical linear model as compared to the theoretical model, because the theoretical model is not always feasible. Overall, we show that estimation of main effects and two-factor interactions, trend-freeness, and minimum cost cannot always be achieved simultaneously. As a consequence, compromise designs have to be considered, which satisfy requirements as much as possible and are practical at the same time. The proposed methods achieve this aim. / Ph. D.

A complexidade de compreensão durante a observação realizada a partir da identificação de um possível quadro de evolução em um sistema climático marcado por uma série temporal longa de uma determinada variável ambiental deve-se ao fato do ambiente sofrer múltiplas interações físico-químicas que naturalmente ocorrem nas escalas global, regional e local. Na intenção de compreender alguns elementos dessa dinâmica foram analisadas algumas hipóteses que podem nos aproximar de possíveis explicações a respeito do contexto que emerge a partir da realidade observada. Neste contexto foi analisada a hipótese de que o ambiente fisicamente alterado pelo homem possa estar influenciado no número de episódios de chuvas nas suas diversas intensidades durante o intervalo de uma hora. A segunda hipótese analisou a possibilidade das alterações em grandes escalas envolvendo às flutuações de temperatura observadas na superfície do mar (TSM) de uma região específica (Niño3.4) localizada no pacífico equatorial possam estar influenciando e/ou intensificando os episódios de chuva em escala local. No entanto, a partir dessas possibilidades o objetivo foi a de analisar através do uso de métodos estatísticos, a partir da aplicação de ajustes e correlações lineares, a identificação de tendências positivas ou negativas, no quadro de cada tipo de chuva e, posteriormente, no quadro das variações de TSM, da região Niño3.4. O segundo procedimento adotado avaliou de uma maneira qualitativa a possibilidade de haver correlações positivas entre os dois ajustes lineares analisados. Os resultados indicaram que a variabilidade climática anual da região Niño3.4 durante a série completa (1970-2009) apresentou um quadro de aquecimento (ajuste positivo). Por outro lado, também foi observado o aquecimento da TSM durante séries específicas da série completa identificadas como fase Neutra, ENOS e La Niña. No entanto, a série especifica relativa à fase El Niño apresentou um comportamento inverso, no caso, um resfriamento na TSM durante o período analisado. Neste caso, foi constatado que o aquecimento anual da TSM da região Niño3.4 ocorre em função do aquecimento observado durante as anomalias negativas (La Niña). O quadro dos ajustes lineares de cada tipo de chuva revelou uma diminuição horária na frequência de chuvas muito fracas (nevoeiros e neblinas), de chuvas fracas (chuviscos e garoas) e de chuvas moderadas (tempestades leves oriundas de nimbostratus). Por outro lado, o quadro de ajustes lineares para chuvas mais intensas foram positivas, como no caso, de chuvas fortes (tempestades ordinárias) e muito fortes (tempestades severas). / The complexity of understanding during the observation carried out from the identification of a possible behavior of evolution in a climatic system marked by a series storm long of a determined environmental variable is due to the fact of the environment suffer multiple interactions chemical-physically what naturally take place in the global, regional and local scales. In the intention of understanding some elements of this dynamic one there were analyzed some hypotheses that can bring near us of possible explanations as to the context that surfaces from the observed reality. In this context it was analyzed the hypothesis of which the environment physically altered by the man could be influenced the number of episodes of rains in his several intensities during the interval of an hour. The second hypothesis analyzed the possibility of the alterations in great scales wrapping to the fluctuations of temperature observed in the surface of the sea (TSM) of a specific region (Niño3.4) located in the Pacific Ocean be able to be influencing and / or intensifying the episodes of rain in local scale. However, from these means the objective was it of analyzing through the use of statistical methods, from the application of agreements and linear correlations, the identification of positive or negative tendencies, in the picture of each type of rain and, subsequently, in the picture of the variations of TSM, of the region Niño3.4. The second adopted proceeding valued in a qualitative way the possibility to be positive correlations between two linear analyzed agreements. The results indicated that the climatic annual variability of the region Niño3.4 during the complete series (1970-2009) presented a picture of heating (positive agreement). On the other side, also the heating of the TSM was observed during specific series, of the complete series, identified like phases Neuter, ENOS and La Niña. However, the series specify relative to the phase El Niño he presented a reverse behavior, in the case, a cooling in the TSM during the analyzed period. In this case, it was noted that the annual heating of the TSM of the region Niño3.4 takes place in function of the heating observed during the negative anomalies (La Niña). The picture of the linear agreements of each type of rain revealed a reduction hourly in the frequency of very weak rains (thick fogs and fogs), of weak rains (drizzles and drizzles) and of moderate rains (light originating storms of nimbostratus). On the other side, the picture of linear agreements for more intense rains they were positive, since in the case, of strong rains (ordinary storms) and very strong (severe storms).

Suppose there is a systematic effect or trend that influences the observations in addition to the block and treatment effects. The problem of experimental designs in the presence of trends was first studied by Cox (1951,1952). Bradley and Yeh (1980) define the concept of trend-free block designs, i.e., the designs in which the analysis of treatment effects are essentially the same whether the trend effects are present or not. If the trend effect within each blocks are the same and linear, Yeh and Bradley (1983) derive a simple necessary condition for designs to be linear trend-free, 　　r_i(k+1)≡0 (mod 2), 1≦i≦v,　　　　　(1) 　　where r_i is the replication of treatment i, for 1≦i≦v, and k is block size. 　　In case where a trend-free version does not exist Yeh et al. (1985) suggest the use of “ nearly trend-free version”. Chai (1995) pays attention to situations where (1) does not hold. He also shows that often, under these circumstances, a nearly linear trend-free design could be constructed. 　　Designs that are derived by extending or deleting m disjoint and binary blocks from BIBD (v,b,k,r,λ)'s are considered. If the resulting designs have linear trend-free versions, by Constantine (1981), they are E-optimal designs with the corresponding classes. When k is even, however, it is impossible to have linear trend-free versions since not all the r_i's are even in such type of designs and (1) is violated. In this paper, we shall convert the designs to be nearly linear trend-free versions of them by permuting the treatment symbols within blocks, and investigate that the resulting designs remain to be E-optimal.

A complexidade de compreensão durante a observação realizada a partir da identificação de um possível quadro de evolução em um sistema climático marcado por uma série temporal longa de uma determinada variável ambiental deve-se ao fato do ambiente sofrer múltiplas interações físico-químicas que naturalmente ocorrem nas escalas global, regional e local. Na intenção de compreender alguns elementos dessa dinâmica foram analisadas algumas hipóteses que podem nos aproximar de possíveis explicações a respeito do contexto que emerge a partir da realidade observada. Neste contexto foi analisada a hipótese de que o ambiente fisicamente alterado pelo homem possa estar influenciado no número de episódios de chuvas nas suas diversas intensidades durante o intervalo de uma hora. A segunda hipótese analisou a possibilidade das alterações em grandes escalas envolvendo às flutuações de temperatura observadas na superfície do mar (TSM) de uma região específica (Niño3.4) localizada no pacífico equatorial possam estar influenciando e/ou intensificando os episódios de chuva em escala local. No entanto, a partir dessas possibilidades o objetivo foi a de analisar através do uso de métodos estatísticos, a partir da aplicação de ajustes e correlações lineares, a identificação de tendências positivas ou negativas, no quadro de cada tipo de chuva e, posteriormente, no quadro das variações de TSM, da região Niño3.4. O segundo procedimento adotado avaliou de uma maneira qualitativa a possibilidade de haver correlações positivas entre os dois ajustes lineares analisados. Os resultados indicaram que a variabilidade climática anual da região Niño3.4 durante a série completa (1970-2009) apresentou um quadro de aquecimento (ajuste positivo). Por outro lado, também foi observado o aquecimento da TSM durante séries específicas da série completa identificadas como fase Neutra, ENOS e La Niña. No entanto, a série especifica relativa à fase El Niño apresentou um comportamento inverso, no caso, um resfriamento na TSM durante o período analisado. Neste caso, foi constatado que o aquecimento anual da TSM da região Niño3.4 ocorre em função do aquecimento observado durante as anomalias negativas (La Niña). O quadro dos ajustes lineares de cada tipo de chuva revelou uma diminuição horária na frequência de chuvas muito fracas (nevoeiros e neblinas), de chuvas fracas (chuviscos e garoas) e de chuvas moderadas (tempestades leves oriundas de nimbostratus). Por outro lado, o quadro de ajustes lineares para chuvas mais intensas foram positivas, como no caso, de chuvas fortes (tempestades ordinárias) e muito fortes (tempestades severas). / The complexity of understanding during the observation carried out from the identification of a possible behavior of evolution in a climatic system marked by a series storm long of a determined environmental variable is due to the fact of the environment suffer multiple interactions chemical-physically what naturally take place in the global, regional and local scales. In the intention of understanding some elements of this dynamic one there were analyzed some hypotheses that can bring near us of possible explanations as to the context that surfaces from the observed reality. In this context it was analyzed the hypothesis of which the environment physically altered by the man could be influenced the number of episodes of rains in his several intensities during the interval of an hour. The second hypothesis analyzed the possibility of the alterations in great scales wrapping to the fluctuations of temperature observed in the surface of the sea (TSM) of a specific region (Niño3.4) located in the Pacific Ocean be able to be influencing and / or intensifying the episodes of rain in local scale. However, from these means the objective was it of analyzing through the use of statistical methods, from the application of agreements and linear correlations, the identification of positive or negative tendencies, in the picture of each type of rain and, subsequently, in the picture of the variations of TSM, of the region Niño3.4. The second adopted proceeding valued in a qualitative way the possibility to be positive correlations between two linear analyzed agreements. The results indicated that the climatic annual variability of the region Niño3.4 during the complete series (1970-2009) presented a picture of heating (positive agreement). On the other side, also the heating of the TSM was observed during specific series, of the complete series, identified like phases Neuter, ENOS and La Niña. However, the series specify relative to the phase El Niño he presented a reverse behavior, in the case, a cooling in the TSM during the analyzed period. In this case, it was noted that the annual heating of the TSM of the region Niño3.4 takes place in function of the heating observed during the negative anomalies (La Niña). The picture of the linear agreements of each type of rain revealed a reduction hourly in the frequency of very weak rains (thick fogs and fogs), of weak rains (drizzles and drizzles) and of moderate rains (light originating storms of nimbostratus). On the other side, the picture of linear agreements for more intense rains they were positive, since in the case, of strong rains (ordinary storms) and very strong (severe storms).

Marketing Mix Modelling has been used since the 1950s, leveraging statistical inference to attribute media investments to sales. Typically, regression models have been used to model the relationship between the two. However, the media landscape evolves at an increasingly rapid pace, driving the need for more refined models which are able to accurately capture these changes. One class of such models are Bayesian structural time series, which are the focal point in this thesis. This class of models retains the relationship between media investments and sales, while also allowing for model parameters to vary over time. The effectiveness of these models is evaluated with respect to prediction accuracy and certainty, both in and out-of-sample. A total of four different models of varying degrees of complexity were investigated. It was concluded that the in-sample performance was similar across models, yet when it came to out-of-sample performance models with time-varying performance outperformed their static counterparts, with respect to uncertainty. Furthermore, the functional form of the intercept influenced the uncertainty of the forecasts on extended time horizons. / Marketing mix modellering har använts sedan 1950-talet för att dra slutsatser om hur mediainvesteringar påverkar försäljning, med hjälp av statistisk inferens. Vanligtvis har regressionmodeller använts för att modellera relationen mellan de två. Men medielandskapet utvecklas allt snabbare, vilket kräver mer sofistikerade modeller som kan fånga upp dessa förändringar på ett mer precist sätt. En klass av sådana modeller är Bayesianska strukturella tidsseriemodeller, som är fokus för detta arbete. Denna klass av modeller bibehåller den strukturella relationen mellan mediainvesteringar och försäljning, samtidigt som de också tillåter modellparametrarna att variera över tid. Effektiviteten hos modellerna bedöms med avseende på noggrannhet och säkerhet, både tränings- och testdata. Totalt fyra olika modeller med varierande komplexitet undersöktes. Det konstaterades att prestandan på träningsdata var likvärdig mellan modellerna, men när det gällde testdata presterade modeller med tidsvarierande parametrar bättre än sina statiska motsvarigheter, med avseende på osäkerhet. Dessutom påverkade den funktionella formen av interceptet osäkerheten hos prognoserna över längre tidshorisonter.

Longitudinal assessments are crucial in evaluating the disease state and trajectory in patients of neurodegenerative diseases. Neuropsychological outcomes measured over time often have a non-linear trajectory with autocorrelated residuals and skewed distributions. Due to these issues, statistical analysis and interpretation involving longitudinal cognitive outcomes can be a difficult and controversial task, thus hindering most convenient transformations (e.g. logarithmic) to avoid the assumption violations of common statistical modelling techniques. We propose the Adjusted Local Linear Trend (ALLT) model, an extended state space model in lieu of the commonly-used linear mixed-effects model (LMEM) in modeling longitudinal neuropsychological outcomes. Our contributed model has the capability to utilize information from the stochasticity of the data while accounting for subject-specific trajectories with the inclusion of covariates and unequally-spaced time intervals. The first step of model fitting involves a likelihood maximization step to estimate the unknown variances in the model before parsing these values into the Kalman Filter and Kalman Smoother recursive algorithms. Results from simulation studies showed that the ALLT model is able to attain lower bias, lower standard errors and high power, particularly in short longitudinal studies with equally-spaced time intervals, as compared to the LMEM. The ALLT model also outperforms the LMEM when data is missing completely at random (MCAR), missing at random (MAR) and, in certain cases, even in data with missing not at random (MNAR). In terms of model selection, likelihood-based inference is applicable for the ALLT model. Although a Chi-Square distribution with k degrees of freedom, where k is the number of parameter lost during estimation, was not the asymptotic distribution in the case of ALLT, we were able to derive an asymptotic distribution approximation of the likelihood ratio test statistics using the power transformation method for the utility of a Gaussian distribution to facilitate model selections for ALLT. In light of these findings, we believe that our proposed model will shed light into longitudinal data analysis not only in the neuropsychological data realm but also on a broader scale for statistical analysis of longitudinal data. / 2023-10-05T00:00:00Z

Detection of structural changes in time series is a topic with increasing pop- ularity among econometricians over the last decades. The main aim of this thesis was to review and compare the classical and modern econometric meth- ods of structural change detection and unit root testing. A recent method for testing a one-time break in at most linear trend function of a series without prior knowledge about the stationary or unit root nature of the error compo- nent proposed by Perron and Yabu (2009b) was studied. Subsequently, it was combined with the unit root test that allows for a break in trend proposed by Kim and Perron (2009) to examine the nature of the error component. All the methods for change detection and unit root testing were compared in a Monte Carlo simulation study that indicated significant improvement in power of the Perron-Yabu and Kim-Perron tests against most alternatives compared to the classical methods. However, all tests demonstrated poor performance in case of a quadratic trend function. Finally, the tests were employed in a practical ex- ample to examine the properties of the quarterly GDP time series of the Czech Republic. 1

Made available in DSpace on 2014-08-20T14:25:52Z (GMT). No. of bitstreams: 1 dissertacao_naile_nunes_vaghetti.pdf: 2548969 bytes, checksum: 7869818d5174fd0ef45be9aa60ebf4b2 (MD5) Previous issue date: 2011-06-10 / The knowledge of relative humidity and its interactions with other variables helps plan of various activities, such as the operation of aeration systems for storing grain and seed, the cooling of environments for breeding and maintenance for environmental comfort. The Rio Grande do Sul state, in function of its geographical position, is a region strongly influenced by meteorological systems, in which the behavior of the relative humidity needs further study. The objective of this work was the study of the relative humidity behavior in the state of Rio Grande do Sul, was used data from monthly averages of 26 meteorological stations in the period 1975 to 2009. For this purpose, the homogeneous regions were determined through analysis of grouping and the grouping method of Ward that has better consistent with the climatic characteristics of the state, in which has been obtained four regions: R1, R2, R3 e R4. For all regions, was made a climatologically study through statistical parameters in order to analyze the climatic variability of this variable. The spatial distribution of relative humidity allowed observing that it has a high pattern in the entire state, being the coastal region the most humid. The relative humidity has only in Regions 2 and 3, a significant linear trend over time, with monthly increase of 0.006% and 0.005%, respectively. During the thirty five years, the monthly increase was 2.52% for the region 2 and 2.1% for the region 3. Was also applied the technique of harmonic analysis to humidity relative data. The proposed models of this harmonic analysis expressed the seasonality of this data with more than 80% of representatively, using for this, two or three sine waves. / O conhecimento da umidade relativa do ar e de suas interações com outras variáveis ajuda no planejamento das mais diversas atividades, tais como: a operação de sistemas de aeração de grãos e sementes armazenadas, a climatização de ambientes para criação de animais e a manutenção do conforto ambiental. O Estado do Rio Grande do Sul (RS), em função de sua posição geográfica, é uma região que sofre bastante a influência de sistemas meteorológicos, sendo que o comportamento da umidade relativa carece de estudos mais aprofundados. O objetivo deste trabalho foi analisar o comportamento da umidade relativa em regiões homogêneas do Estado do Rio Grande do Sul, utilizando dados de médias mensais de 26 estações meteorológicas, do período de 1975 a 2009. Para isto, foram determinadas regiões homogêneas por meio da Análise de Agrupamento, sendo utilizado como método de agrupamento o método de Ward, o qual mostrou a melhor coerência com as características climáticas do Estado, sendo obtidas quatro regiões: R1, R2, R3 e R4. Para todas as regiões, fez-se um estudo climatológico através de parâmetros estatísticos com a finalidade de se observar a variabilidade climática desta variável. A distribuição espacial da umidade relativa permitiu observar que esta tem um padrão elevado em todo o Estado, sendo a região litorânea a mais úmida. A umidade relativa apresenta, somente nas Regiões 2 e 3, tendência linear significativa ao longo do tempo, com aumentos mensais de 0,006% e 0,005%, respectivamente. O longo dos 35 anos, o aumento mensal total foi de 2,52% para a Região 2 e 2,1% para a Região 3. Aplicou-se também aos dados de umidade relativa a técnica de análise harmônica. Os modelos propostos por esta análise harmônica expressaram a sazonalidade dos dados com mais de 80% de representatividade, utilizando para isto, duas ou três ondas senoidais.

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Diese Dissertation beinhaltet vier Aufsätze, die zur Literatur der Panelkointegrationsmethodik beitragen. Der erste Aufsatz vergleicht die Eigenschaften der vier Residuen-basierten Panelkointegrationstests von Pedroni (1995, 1999) mit dem Likelihood-basierten Panelkointegrationstest von Larsson et al. (2001) in endlichen Stichproben. Die Simulationsergebnisse zeigen, dass unter den fünf untersuchten Panelkointegrationsteststatistiken die Panel-t Teststatistik von Pedroni (1995, 1999) die besten Eigenschaften in endlichen Stichproben besitzt. Der zweite Aufsatz präsentiert eine Korrektur des Beweises von Larsson et al. (2001) bezüglich der Endlichkeit der Momente der asymptotischen Trace-Statistik für den Fall, dass die Differenz zwischen der Anzahl der Variablen und der Anzahl der existierenden Kointegrationsbeziehungen eins ist. Im dritten Aufsatz wird ein neuer Likelihood-basierter Panelkointegrationstest vorgestellt, der die Existenz eines linearen Trends in dem datengenerierenden Prozess erlaubt. Dieser neue Test ist eine Erweiterung des Likelihood-Quotienten-Tests von Saikkonen und Lütkepohl (2000a) für trendbereinigte Daten auf die Paneldatenanalyse. Unter der Nullhypothese folgt die Panel-SL Teststatistik einer standardisierten Normalverteilung, wenn die Anzahl der Beobachtungen über die Zeit (T) und die Anzahl der Querschnitte (N) sequentiell gegen unendlich gehen. In einer Monte-Carlo-Studie werden die Eigenschaften des Panel-SL Tests in endlichen Stichproben untersucht. Der neue Test hat ein annehmbares empirisches Signifikanzniveau für wachsende T und N sowie eine hohe Güte in kleinen Stichproben. Der letzte Aufsatz der Dissertation analysiert die langfristige Geldnachfragefunktion in OECD Ländern mit Hilfe von Paneleinheitswurzel- und Panelkointegrationstests. Um eine mögliche Existenz einer stationären langfristigen Geldnachfragefunktion zu untersuchen, werden der Panel-SL Kointegrationstest und die Tests von Pedroni (1999) verwendet. Im Anschluss daran wird eine Paneldatenschätzung für die Geldnachfragefunktion mittels der dynamischen Kleinste-Quadrate-Methode von Mark und Sul (2003) durchgeführt. / This thesis is composed of four essays which contribute to the literature in panel cointegration methodology. The first essay compares the finite sample properties of the four residual-based panel cointegration tests of Pedroni (1995, 1999) and the likelihood-based panel cointegration test of Larsson et al. (2001). The simulation results indicate that the panel-t test statistic of Pedroni has the best finite sample properties among the five panel cointegration test statistics evaluated. The second essay presents a corrected version of the proof of Larsson et al. (2001) related to the finiteness of the moments of the asymptotic trace statistic. The proof is corrected for the case, in which the difference between the number of variables and the number of existing cointegrating relations is one. The third essay proposes a new likelihood-based panel cointegration test in the presence of a linear time trend in the data generating process. This new test is an extension of the likelihood ratio test of Saikkonen and Lütkepohl (2000) for trend-adjusted data to the panel data framework, and is called the panel SL test. Under the null hypothesis, the panel SL test statistic is standard normally distributed as the number of time periods (T) and the number of cross-sections (N) tend to infinity sequentially. By means of a Monte Carlo study the finite sample properties of the test are investigated. The new test presents reasonable size with the increase in T and N, and has high power in small samples. The last essay of the thesis analyzes the long-run money demand relation among OECD countries by panel unit root and cointegration testing techniques. The panel SL cointegration test and the tests of Pedroni (1999) are used to detect the existence of a stationary long-run money demand relation. Moreover, the money demand function is estimated with the panel dynamic ordinary least squares method of Mark and Sul (2003).