This dissertation investigates the interactive or joint influence of autocorrelative processes (autoregressive-AR, moving average-MA, and autoregressive moving average-ARMA) and sample weights present in a longitudinal panel data set. Specifically, to what extent are the sample estimates influenced when autocorrelation (which is usually present in a panel data having correlated observations and errors) and sample weights (complex sample design feature used in longitudinal data having multi-stage sampling design) are modeled versus when they are not modeled or either one of them is taken into account. The current study utilized a Monte Carlo simulation design to vary the type and magnitude of autocorrelative processes and sample weights as factors incorporated in growth or latent curve models to evaluate the effect on sample latent curve estimates (mean intercept, mean slope, intercept variance, slope variance, and intercept slope correlation). Various latent curve models with weights or without weights were specified with an autocorrelative process and then fitted to data sets having either the AR, MA or ARMA process. The relevance and practical importance of the simulation results were ascertained by testing the joint influence of autocorrelation and weights on the Early Childhood Longitudinal Study for Kindergartens (ECLS-K) data set which is a panel data set having complex sample design features. The results indicate that autocorrelative processes and weights interact with each other as sources of error to a statistically significant degree. Accounting for just the autocorrelative process without weights or utilizing weights while ignoring the autocorrelative process may lead to bias in the sample estimates particularly in large-scale datasets in which these two sources of error are inherently embedded. The mean intercept and mean slope of latent curve models without weights was consistently underestimated when fitted to data sets having AR, MA or ARMA process. On the other hand, the intercept variance, intercept slope, and intercept slope correlation were overestimated for latent curve models with weights. However, these three estimates were not accurate as the standard errors associated with them were high. In addition, fit indices, AR and MA estimates, parsimony of the model, behavior of sample latent curve estimates, and interaction effects between autocorrelative processes and sample weights should be assessed for all the models before a particular model is deemed as most appropriate. If the AR estimate is high and MA estimate is low for a LCAR model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an AR process between the observations. If the MA estimate is high and AR estimate is low for a LCMA model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an MA process between the observations. If both AR and MA estimates are high for a LCARMA model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an ARMA process between the observations. The results from the current study recommends that biases from both autocorrelation and sample weights needs to be simultaneously modeled to obtain accurate estimates. The type of autocorrelation (AR, MA or ARMA), magnitude of autocorrelation, and sample weights influences the behavior of estimates and all the three facets should be carefully considered to correctly interpret the estimates especially in the context of measuring growth or change in the variable(s) of interest over time in large-scale longitudinal panel data sets.

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L'optimisation d'une opération de mélange de poudre repose essentiellement sur un travail expérimental à l'échelle du laboratoire qui doit pouvoir être transposer aux mélangeurs de plus grandes tailles. Définir des lois d'extrapolation et améliorer notre connaissance de la dynamique du mélange est donc nécessaire. Dans ces travaux, la dynamique de mélange au sein des mélangeurs Turbula® a été étudiée en s'appuyant sur l'analyse des cinétiques de mélange et des fonctions d'autocorrélation pour plusieurs systèmes particulaires. Selon les vitesses de rotation de l'axe moteur, 3 régimes d'écoulement ont été définis et les principaux mécanismes de mélange et de ségrégation apparaissant pour chacun de ces régimes ont été identifiés en lien avec les propriétés d'écoulement des produits. Dans un deuxième temps, les qualités de mélange obtenues dans différentes tailles de mélangeurs ont été comparées sur la base du principe des similitudes afin de mettre en évidence les facteurs ayant une influence lors du passage d'une taille de mélangeur à une autre. Enfin dans le cadre d'une application industrielle, une méthodologie s'appuyant sur l'intensité de ségrégation et l'autocorrélation spatiale, a été développée pour identifier des défauts d'homogénéité au sein de plaques bipolaires composites / The optimization of a powder mixing step typically involves an experimental work at lab scale in order to be transposed to larger mixers. Defining scale-up laws and improving our knowledge of the mixing dynamics remains some of the mains industrial issues of this century. In this work, the mixing dynamics of several particulate systems has been studied in Turbula mixers thanks to the analysis of mixing kinetics and autocorrelation functions. According to the engine speed, three flow regimes have been defined. The corresponding main mixing and segregation mechanisms at play for each of these regimes have been identified in relation with the flow properties of the products. In a second phase, the qualities of the mixtures obtained in the different mixer sizes have been compared on the basis of the principle of similarities in order to shed light the factors which influencing scale-up. Finally, as part of an industrial application, a methodology has been developed using the concept of intensity of segregation and the spatial autocorrelation tools to identify heterogeneities in bipolar plates made of composite materials

In this thesis, identification of periodically varying orders of univariate Periodic Autoregressive Moving-Average (PARMA) processes is mainly studied. The identification of the varying orders of PARMA process is carried out by generalizing the well-known Box-Jenkins techniques to a seasonwise manner. The identification of pure periodic moving-average (PMA) and pure periodic autoregressive (PAR) models are considered only. For PARMA model identification, the Periodic Autocorrelation Function (PeACF) and Periodic Partial Autocorrelation Function (PePACF), which play the same role as their ARMA counterparts, are employed. For parameter estimation, which is considered only to refine model identification, the conditional least squares estimation (LSE) method is used which is applicable to PAR models. Estimation becomes very complicated, difficult and may give unsatisfactory results when a moving-average (MA) component exists in the model. On account of overcoming this difficulty, seasons following PMA processes are tried to be modeled as PAR processes with reasonable orders in order to employ LSE. Diagnostic checking, through residuals of the fitted model, is also performed stating its reasons and methods. The last part of the study demonstrates application of identification techniques through analysis of two seasonal hydrologic time series, which consist of average monthly streamflows. For this purpose, computer programs were developed specially for PARMA model identification.

Longitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data. Biased inference can occur in linear mixed-effects modelling if subjects are drawn from a number of unknown sub-populations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a two-step approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially non-monotonic variance and correlation functions. Spatially explicit capture-recapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multi-occasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radio-tagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animal-level covariates.

Several studies in hydrology have reported differences in outcomes between models in which spatial autocorrelation (SAC) is accounted for and those in which SAC is not. However, the capacity to predict the magnitude of such differences is still ambiguous. In this thesis, I hypothesized that SAC, inherently possessed by a response variable, influences spatial modeling outcomes. I selected ten watersheds in the USA and analyzed them to determine whether water quality variables with higher Moran’s I values undergo greater increases in the coefficient of determination (R²) and greater decreases in residual SAC (rSAC) after spatial modeling. I compared non-spatial ordinary least squares to two spatial regression approaches, namely, spatial lag and error models. The predictors were the principal components of topographic, land cover, and soil group variables. The results revealed that water quality variables with higher inherent SAC showed more substantial increases in R² and decreases in rSAC after performing spatial regressions. In this study, I found a generally linear relationship between the spatial model outcomes (R² and rSAC) and the degree of SAC in each water quality variable. I suggest that the inherent level of SAC in response variables can predict improvements in models before spatial regression is performed. The benefits of this study go beyond modeling selection and performance, it has the potential to uncover hydrologic connectivity patterns that can serve as insights to water quality managers and policy makers.

This volume is a collection of three essays relating to the pricing of securities in financial markets, such as stock markets, where a large number of individual securities are traded. Lead-Lag Effects in a Competitive REE MarketThis essay introduces a model of cross-security information aggregation. The model is essentially an extension of Chan (Journal of Finance, 1993) to the case of simultaneous auction markets where revealed information is correlated across securities.The model provides clear predictions of lead-lag effects between securities returns. Several of the model's predictions are confirmed empirically using data from the Paris Bourse. Other models of price formation, including the basic Chan model and nonsynchronous trading, are rejected as they cannot account for observed return patterns. Learning the True Index LevelThis essay extends the model of cross-security information aggregation by deriving implications for autocorrelation in index returns. Both time series and cross-sectional predictions are confirmed by empirical evidence from the Paris Bourse. In addition, the time series predictions are consistent with earlier, partly unexplained, empirical evidence from the US market. An Empirical Study of Index Return AutocorrelationThis essay studies return autocorrelation on the Stockholm Stock Exchange focusing on the relation between index returns and indvidual stock returns. It is demonstrated that the two return types have similar time series properties, and it is concluded that the causes of autocorrelation are the same in both cases. / <p>Diss. Stockholm : Handelshögskolan, 1997</p>