For the empirical macroeconomist, accounting for nonlinearities in data series by using regime switching techniques has a long history. Over the past 25 years, there have been tremendous advances in both the estimation of regime switching and the incorporation of regime switching into macroeconomic models. In this dissertation, I apply techniques from this literature to study two topics that are of particular relevance to the conduct of monetary policy: asset bubbles and the Federal Reserve’s policy reaction function. My first chapter utilizes a recently developed Markov-Switching model in order to test for asset bubbles in simulated data. I find that this flexible model is able to detect asset bubbles in about 75% of simulations. In my second and third chapters, I focus on the Federal Reserve’s policy reaction function. My second chapter advances the literature in two important directions. First, it uses meeting- based timing to more properly account for the target Federal Funds rate; second, it allows for the inclusion of up to 14 economic variables. I find that the long-run inflation response coefficient is larger than had been found in previous studies, and that increasing the number of economic variables that can enter the model improves both in-sample fit and out-of-sample forecasting ability. In my third chapter, I introduce a new econometric model that allows for Markov-Switching, but can also remove variables from the model, or enforce a restriction that there is no regime switching. My findings indicate that the majority of coefficients in the Federal Reserve’s policy reaction function have not changed over time.

The Gaussian mixture model has been used for model-based clustering analysis for decades. Most model-based clustering analyses are based on the Gaussian mixture model. Model averaging approaches for Gaussian mixture models are proposed by Wei and McNicholas, based on a family of 14 Gaussian parsimonious clustering models. In this thesis, we use non-Gaussian mixture models, namely the tEigen family, for our averaging approaches. This paper studies fitting in an averaged model from a set of multivariate t-mixture models instead of fitting a best model. / Thesis / Master of Science (MSc)

This thesis studies the problem of frequentist model averaging over a set of multiple $\epsilon$-support vector regression (SVR) models, where the support vector machine (SVM) algorithm was extended to function estimation involving continuous targets, instead of categorical ones. By assigning weights to a set of candidate models instead of selecting the least misspecified one, model averaging presents a strong alternative to model selection for tackling model uncertainty. Not only do we describe the construction of smoothed BIC/AIC model averaging weights, but we also propose a Mallows model averaging procedure which selects model weights by minimizing Mallows' criterion. We conduct two studies where the set of candidate models can either include or not include the true model by making use of simulated random samples obtained from different data-generating processes of analytic form. In terms of mean squared error, we demonstrate that our proposed method outperforms other model averaging and model selection methods that were tested, and the gain is more substantial for smaller sample sizes with larger signal-to-noise ratios. / Thesis / Master of Science (MSc)

The primary aim of this research is to shed more light on the issue of model uncertainty in applied econometrics in general and cross-country growth as well as happiness and well-being regressions in particular. Model uncertainty consists of three main types: theory uncertainty, focusing on which principal determinants of economic growth or happiness should be included in a model; heterogeneity uncertainty, relating to whether or not the parameters that describe growth or happiness are identical across countries; and functional form uncertainty, relating to which growth and well-being regressors enter the model linearly and which ones enter nonlinearly. Model averaging methods including Bayesian model averaging and Frequentist model averaging are the main statistical tools that incorporate theory uncertainty into the estimation process. To address functional form uncertainty, a variety of techniques have been proposed in the literature. One suggestion, for example, involves adding regressors that are nonlinear functions of the initial set of theory-based regressors or adding regressors whose values are zero below some threshold and non-zero above that threshold. In recent years, however, there has been a rising interest in using nonparametric framework to address nonlinearities in growth and happiness regressions. The goal of this research is twofold. First, while Bayesian approaches are dominant methods used in economic empirics to average over the model space, I take a fresh look into Frequentist model averaging techniques and propose statistical routines that computationally ease the implementation of these methods. I provide empirical examples showing that Frequentist estimators can compete with their Bayesian peers. The second objective is to use recently-developed nonparametric techniques to overcome the issue of functional form uncertainty while analyzing the variance of distribution of per capita income. Nonparametric paradigm allows for addressing nonlinearities in growth and well-being regressions by relaxing both the functional form assumptions and traditional assumptions on the structure of error terms. / Ph. D.

The fossil record is the primary source of information on the history of life. As such, it is important to understand the limitations of this record. One critical area in which there is still much work to be done is in understanding how the fossil record, and our interpretation of it, may be biased. Herein, the fidelity between the life and death assemblage of an extant brachiopod with respect to morphological variability is studied using geometric morphometrics. The results from several analyses confirm a high degree of morphological variability with little change in mean shape between the living and sub-fossil assemblage. Additionally, there is no evidence of distinct morphogroups in either assemblage. These trends persist at all depths and size classes indicating that this species could be recognized as a single, rather than multiple, species if only fossil data were available. The second chapter involves the recognition and quantification of a worker bias in monographs of brachiopods and bivalves. Most specimens studied came from the 65th to 69th percentile of their species' bulk-collected size-frequency distribution. This indicates a significant bias toward monograph specimens that are larger than the mean size of the bulk sample. When compared at the species level, this bias was found to be highly consistent among the 86 species included in the study. Thus, size measurements of monographed specimens reliably and consistently record a similar size class for any given species, and this bias is easily corrected during meta-analyses. Chapter three focuses on bivalves and brachiopods from a modern tropical shelf and quantifies the magnitude of time averaging (temporal mixing) for these two different organisms. This is accomplished by dating a suite of shells from each site using amino acid racemization calibrated with several radiocarbon dates. By studying the age distributions for each species it is determined that, despite some site to site differences, both bivalve and brachiopod species exhibit a similar time averaging magnitude when collected from the same region or depositional system. This indicates that fossil assemblages of these species may have very similar resolution. / Ph. D.

The contributions of this dissertation can be divided into three primary foci: input waveform optimization, the modeling and optimization of fish-like robots, and experiments on a flapping wing robot. Novel contributions were made in every focus. The first focus was on input waveform optimization. This goal of this research was to develop a means by which the optimal input waveforms can be selected to vibrationally stabilize a system. Vibrational stabilization is the use of high-frequency, high-amplitude periodic waveforms to stabilize a system about a desired state. The contributions presented herein develop a technique to choose the ``best" input waveform and a discussion of how the ``best" input waveform changes with the definition of ``best." The next focus was the optimization of a fish-like robot. In order to optimize such robots, a new model for fish-like locomotion is developed. An optimization technique that uses numerous simulations of fish-like locomotion was used to determine the best gaits for traveling at various speeds. Based on these results, trends were found that can determine the optimal gait using a couple relatively simple functions. The final focus was experimentation on a flapping wing robot in a wind tunnel. These experiments determined the performance of the flapping wing robot at a variety of flight conditions. The results of this research were presented in manner that is accessible to the larger aircraft design community rather than only to those specializing in flapping flight. / Ph. D.

Control of underactuated mechanical systems is of interest as it allows for control authority over all of a system's degrees of freedom without requiring actuation of the full system. In addition to this, open-loop control of a system provides the advantage of applying to systems with unmeasurable states or where sensor integration is not feasible. Vibrational control is an open-loop control strategy that uses high-frequency, high-amplitude forcing to control underactuated mechanical systems. This thesis is concerned with exploring two underactuated mechanical systems that are controlled using vibrational inputs. The first system, a 3 degrees of freedom (DOFs) 2-link mechanism with 1 actuated DOF which is an example of a vibrational control system with 1 input and 2 unactuated DOFs, is used to review analytical results of stability analysis using the averaged potential. Theoretical and numerical results are presented for the achievable stable configurations of the system and the effects of changing the physical parameters on the achievable stable configurations are studied. The primary contribution of this effort is the development of an experimental apparatus where vibrational control is implemented. The second system is a 4DOF system composed of a 2DOF spherical pendulum supported by an actuated 2DOF cart used to study the effects of multiple vibrational inputs acting on a system. Theoretical and numerical analysis results are presented for three variants of harmonic forcing applied to the two actuated degrees of freedom: 1) identical input waveforms, except for the amplitudes, 2) identical input waveforms, except for the amplitudes and a phase shift, and 3) identical input waveforms, but at different frequencies and amplitudes. The equilibrium sets under open-loop vibrational forcing are determined for all three cases. A general closed-loop vibrational control scheme is presented using proportional feedback of the unactuated coordinates superposed with the zero-mean, $T$-periodic vibrational input. / M.S. / Underactuated mechanical systems are systems where the driven degrees of freedom are fewer than the total degrees of freedom of the system. These systems can be controlled using vibrational control which is an open-loop control strategy that uses high-frequency, high-amplitude forcing to control the states of a system. An open-loop control strategy is one in which there are no measurements of the system states required in the control scheme. This allows for control of systems where sensor integration is not feasible. This thesis is concerned with exploring vibrational control of two underactuated mechanical systems. The stability of the equilibrium sets of these systems is assessed using the averaged potential, which is an energy-like quantity used to determine stability of equilibria of systems with high-frequency inputs. Theoretical and numerical results are presented for both systems and the effects of physical parameters and variants of harmonic forcing on the achievable stable configurations of the systems are studied. The two main contributions of the thesis are the development of an experimental apparatus where vibrational control is physically implemented for one system and the outline of the closed-loop vibrational control scheme.

Um dos mais investigados problemas na teoria qualitativa dos sistemas dinâmicos no plano é o XVI problema de Hilbert que investiga uma cota superior para o número de ciclos limites em sistemas diferenciais polinomiais e suas posições relativas. Por outro lado, os sistemas diferenciais suaves por partes tem despertado o interesse de muitos pesquisadores recentemente devido a sua estreita relação com outras áreas das ciências como física, biologia, economia e engenharias. Portanto é natural a busca pela extensão das técnicas e ferramentas da teoria qualitativa para essa classe de sistemas. Nessa dissertação apresentamos uma generalização da técnica do averaging para uma classe especial dos sistemas de Filippov, conhecida como sistemas diferenciais contínuos por partes, desenvolvida por Llibre-Novaes-Teixeira e, aplicamos essa técnica na investigação de uma classe particular de sistemas, que chamamos do tipo Kukles generalizado. / One of the most investigated problems in the qualitative theory of dynamical systems in the plane is the XVI Hilbert\'s problem which asks for the maximum number and position of limity cycles for all planar polynomial differential systems of degree n. On the other hand, recently piecewise continuous differential systems have attracting the interest of many researches specially because of their close relation with other sciences for instance physics, biology, economy and engineering. These relations motivate extensions of the qualitative tools for this class of systems. In this work we present a generalization of the averaging theory for a class of Filippov systems, namely piecewise continuous differential systems, developed by Llibre-Novaes-Teixeira and, we apply this theory to a particular class of differential systems, which we nominate generalized Kukles type.

nÃo hà / O presente trabalho busca investigar eventual relaÃÃo entre o desenvolvimento financeiro e desigualdade de renda. Para tal, foram utilizados os dados dos 184 municÃpios cearenses, para o ano de 2010, firmando-se como medida de desigualdade o Ãndice de Gini e, como variÃveis explicativas, as razÃes estabelecidas entre crÃdito e PIB, entre operaÃÃes de crÃdito e PIB; entre operaÃÃes de crÃdito e populaÃÃo; entre financiamentos e PIB e, por fim, entre financiamentos e populaÃÃo, como proxies para o desenvolvimento financeiro. Foi utilizado o mÃtodo denominado Jackknife Model Averaging, que se caracteriza por ser um procedimento de estimaÃÃo que leva em consideraÃÃo todas as possÃveis especificaÃÃes de modelo com base em um conjunto de variÃveis. Empregou-se, ainda, a abordagem FMA, sugerida em Hansen e Racine (2012). Os resultados obtidos indicam que o desenvolvimento financeiro nÃo à estatisticamente relevante para interferir na reduÃÃo da desigualdade de renda. / This work seeks to investigate an eventual relationship between financial development and income inequality. For this, was used data from 184 cities from CearÃ, at the year of 2010, Using as a measure of inequality, the Gini index and, as explanatory variables, the reasons established between credit and GDP, between credit and GDP operations; between credit and population operations; between financing and GDP and, finally, between funding and population, as proxies for financial development. Was used the method called Jackknife Model Averaging, which is characterized by being a procedure of estimation that takes into account all possible model specifications based on a set of variables. We used also the FMA approach suggested in Hansen and Racine (2012). The results indicate that financial development is not statistically relevant to interfere in reducing income inequality.

Um dos mais investigados problemas na teoria qualitativa dos sistemas dinâmicos no plano é o XVI problema de Hilbert que investiga uma cota superior para o número de ciclos limites em sistemas diferenciais polinomiais e suas posições relativas. Por outro lado, os sistemas diferenciais suaves por partes tem despertado o interesse de muitos pesquisadores recentemente devido a sua estreita relação com outras áreas das ciências como física, biologia, economia e engenharias. Portanto é natural a busca pela extensão das técnicas e ferramentas da teoria qualitativa para essa classe de sistemas. Nessa dissertação apresentamos uma generalização da técnica do averaging para uma classe especial dos sistemas de Filippov, conhecida como sistemas diferenciais contínuos por partes, desenvolvida por Llibre-Novaes-Teixeira e, aplicamos essa técnica na investigação de uma classe particular de sistemas, que chamamos do tipo Kukles generalizado. / One of the most investigated problems in the qualitative theory of dynamical systems in the plane is the XVI Hilbert\'s problem which asks for the maximum number and position of limity cycles for all planar polynomial differential systems of degree n. On the other hand, recently piecewise continuous differential systems have attracting the interest of many researches specially because of their close relation with other sciences for instance physics, biology, economy and engineering. These relations motivate extensions of the qualitative tools for this class of systems. In this work we present a generalization of the averaging theory for a class of Filippov systems, namely piecewise continuous differential systems, developed by Llibre-Novaes-Teixeira and, we apply this theory to a particular class of differential systems, which we nominate generalized Kukles type.