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<p>This dissertation is a collection of four essays on nonstationary time series econometrics, which are grouped into four chapters. The first chapter investigates the inference in mildly explosive autoregressions under unconditional heteroskedasticity. The second chapter develops a new approach to forecasting a highly persistent time series that employs feasible generalized least squares (FGLS) estimation of the deterministic components in conjunction with Mallows model averaging. The third chapter proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by nonstationary volatility. The last chapter studies the problem of testing partial parameter stability in cointegrated regression models.</p>

This dissertation is organized into three independent chapters. In Chapter 1, I consider the selection of weights for averaging a set of threshold models. Existing model averaging literature primarily focuses on averaging linear models, I consider threshold regression models. The theory I developed in that chapter demonstrates that the proposed jackknife model averaging estimator achieves asymptotic optimality when the set of candidate models are all misspecified threshold models. The simulations study demonstrates that the jackknife model averaging estimator achieves the lowest mean squared error when contrasted against other model selection and model averaging methods. In Chapter 2, I propose a model averaging framework for the synthetic control method of Abadie and Gardeazabal (2003) and Abadie et al. (2010). The proposed estimator serves a twofold purpose. First, it reduces the bias in estimating the weights each member of the donor pool receives. Secondly, it accounts for model uncertainty for the program evaluation estimation. I study two variations of the model, one where model weights are derived by solving a cross-validation quadratic program and another where each candidate model receives equal weights. Next, I show how to apply the placebo study and the conformal inference procedure for both versions of my estimator. With a simulation study, I reveal that the superior performance of the proposed procedure. In Chapter 3, which is co-authored with my advisor Professor Youngki Shin, we provide an exact computation algorithm for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all indicator functions into binary parameters to be estimated and show that the transformation is equivalent to the original problem. Using a modern MIP solver, we apply the proposed method to an empirical example and Monte Carlo simulations. The results show that the proposed algorithm performs better than the existing alternatives. / Dissertation / Doctor of Philosophy (PhD)

Yes / The use of the Advanced Censored Closure (ACC) technique, recently proposed by the authors for predicting the peak response of linear structures vibrating under random processes, is extended to the case of non-linear oscillators driven by stationary white noise. The proposed approach requires the knowledge of mean upcrossing rate and spectral bandwidth of the response process, which in this paper are estimated through the Stochastic Averaging method. Numerical applications to oscillators with non-linear stiffness and damping are included, and the results are compared with those given by Monte Carlo Simulation and by other approximate formulations available in the literature.

Posterior analysis in Bayesian model averaging (BMA) applications often includes the assessment of measures of jointness (joint inclusion) across covariates. We link the discussion of jointness measures in the econometric literature to the literature on association rules in data mining exercises. We analyze a group of alternative jointness measures that include those proposed in the BMA literature and several others put forward in the field of data mining. The way these measures address the joint exclusion of covariates appears particularly important in terms of the conclusions that can be drawn from them. Using a dataset of economic growth determinants, we assess how the measurement of jointness in BMA can affect inference about the structure of bivariate inclusion patterns across covariates. (authors' abstract) / Series: Department of Economics Working Paper Series

L’intérêt principal de cette recherche porte sur la validation d’une méthode statistique en pharmaco-épidémiologie. Plus précisément, nous allons comparer les résultats d’une étude précédente réalisée avec un devis cas-témoins niché dans la cohorte utilisé pour tenir compte de l’exposition moyenne au traitement : – aux résultats obtenus dans un devis cohorte, en utilisant la variable exposition variant dans le temps, sans faire d’ajustement pour le temps passé depuis l’exposition ; – aux résultats obtenus en utilisant l’exposition cumulative pondérée par le passé récent ; – aux résultats obtenus selon la méthode bayésienne. Les covariables seront estimées par l’approche classique ainsi qu’en utilisant l’approche non paramétrique bayésienne. Pour la deuxième le moyennage bayésien des modèles sera utilisé pour modéliser l’incertitude face au choix des modèles. La technique utilisée dans l’approche bayésienne a été proposée en 1997 mais selon notre connaissance elle n’a pas été utilisée avec une variable dépendante du temps. Afin de modéliser l’effet cumulatif de l’exposition variant dans le temps, dans l’approche classique la fonction assignant les poids selon le passé récent sera estimée en utilisant des splines de régression. Afin de pouvoir comparer les résultats avec une étude précédemment réalisée, une cohorte de personnes ayant un diagnostique d’hypertension sera construite en utilisant les bases des données de la RAMQ et de Med-Echo. Le modèle de Cox incluant deux variables qui varient dans le temps sera utilisé. Les variables qui varient dans le temps considérées dans ce mémoire sont iv la variable dépendante (premier évènement cérébrovasculaire) et une des variables indépendantes, notamment l’exposition / The main interest of this research is the validation of a statistical method in pharmacoepidemiology. Specifically, we will compare the results of a previous study performed with a nested case-control which took into account the average exposure to treatment to : – results obtained in a cohort study, using the time-dependent exposure, with no adjustment for time since exposure ; – results obtained using the cumulative exposure weighted by the recent past ; – results obtained using the Bayesian model averaging. Covariates are estimated by the classical approach and by using a nonparametric Bayesian approach. In the later, the Bayesian model averaging will be used to model the uncertainty in the choice of models. To model the cumulative effect of exposure which varies over time, in the classical approach the function assigning weights according to recency will be estimated using regression splines. In order to compare the results with previous studies, a cohort of people diagnosed with hypertension will be constructed using the databases of the RAMQ and Med-Echo. The Cox model including two variables which vary in time will be used. The time-dependent variables considered in this paper are the dependent variable (first stroke event) and one of the independent variables, namely the exposure.

In risk analysis, Benchmark dose (BMD)methodology is used to quantify the risk associated with exposure to stressors such as environmental chemicals. It consists of fitting a mathematical model to the exposure data and the BMD is the dose expected to result in a pre-specified response or benchmark response (BMR). Most available exposure data are from single chemical exposure, but living objects are exposed to multiple sources of hazards. Furthermore, in some studies, researchers may observe multiple endpoints on one subject. Statistical approaches to address multiple endpoints problem can be partitioned into a dimension reduction group and a dimension preservative group. Composite scores using desirability function is used, as a dimension reduction method, to evaluate neurotoxicity effects of a mixture of five organophosphate pesticides (OP) at a fixed mixing ratio ray, and five endpoints were observed. Then, a Bayesian hierarchical model approach, as a single unifying dimension preservative method is introduced to evaluate the risk associated with the exposure to mixtures chemicals. At a pre-specied vector of BMR of interest, the method estimates a tolerable area referred to as benchmark dose tolerable area (BMDTA) in multidimensional Euclidean plan. Endpoints defining the BMDTA are determined and model uncertainty and model selection problems are addressed by using the Bayesian Model Averaging (BMA) method.

If policymakers address water scarcity with the demand-oriented approach, the income elasticity of water demand is of pivotal importance. Its estimates, however, differ considerably. We collect 307 estimates of the income elasticity of water demand reported in 62 studies, codify 31 variables describing the estimation design, and employ Bayesian model averaging to address model uncertainty inherent to any meta-analysis. The studies were published between 1972 and 2015, which means that this meta-analysis covers a longer period of time than two previous meta-analyses on this topic combined. Our results suggest that income elasticity estimates for developed countries do not significantly differ from income elasticity estimates for developing countries and that different estimation techniques do not systematically produce different values of the income elasticity of water demand. We find evidence of publication selection bias in the literature on the income elasticity of water demand with the use of both graphical and regression analysis. We correct the estimates for publication selection bias and estimate the true effect beyond bias, which reaches approximately 0.2. 1