Theses and Dissertations

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Browsing Theses and Dissertations by Author "Cox, Dennis D."

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    An Approach for the Adaptive Solution of Optimization Problems Governed by Partial Differential Equations with Uncertain Coefficients
    (2012-09-05) Kouri, Drew; Heinkenschloss, Matthias; Sorensen, Danny C.; Riviere, Beatrice M.; Cox, Dennis D.
    Using derivative based numerical optimization routines to solve optimization problems governed by partial differential equations (PDEs) with uncertain coefficients is computationally expensive due to the large number of PDE solves required at each iteration. In this thesis, I present an adaptive stochastic collocation framework for the discretization and numerical solution of these PDE constrained optimization problems. This adaptive approach is based on dimension adaptive sparse grid interpolation and employs trust regions to manage the adapted stochastic collocation models. Furthermore, I prove the convergence of sparse grid collocation methods applied to these optimization problems as well as the global convergence of the retrospective trust region algorithm under weakened assumptions on gradient inexactness. In fact, if one can bound the error between actual and modeled gradients using reliable and efficient a posteriori error estimators, then the global convergence of the proposed algorithm follows. Moreover, I describe a high performance implementation of my adaptive collocation and trust region framework using the C++ programming language with the Message Passing interface (MPI). Many PDE solves are required to accurately quantify the uncertainty in such optimization problems, therefore it is essential to appropriately choose inexpensive approximate models and large-scale nonlinear programming techniques throughout the optimization routine. Numerical results for the adaptive solution of these optimization problems are presented.
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    Essays in Structural Econometrics of Auctions
    (2012-09-05) Bulbul Toklu, Seda; Sickles, Robin C.; Medlock, Kenneth B., III; Cox, Dennis D.
    The first chapter of this thesis gives a detailed picture of commonly used structural estimation techniques for several types of auction models. Next chapters consist of essays in which these techniques are utilized for empirical analysis of auction environments. In the second chapter we discuss the identification and estimation of the distribution of private signals in a common value auction model with an asymmetric information environment. We argue that the private information of the informed bidders are identifiable due to the asymmetric information structure. Then, we propose a two stage estimation method, which follows the identification strategy. We show, with Monte-Carlo experiments, that the estimator performs well. Third chapter studies Outer Continental Shelf drainage auctions, where oil and gas extraction leases are sold. Informational asymmetry across bidders and collusive behavior of informed firms make this environment very unique. We apply the technique proposed in the second chapter to data from the OCS drainage auctions. We estimate the parameters of a structural model and then run counterfactual simulations to see the effects of the informational asymmetry on the government's auction revenue. We find that the probability that information symmetry brings higher revenue to the government increases with the value of the auctioned tract. In the fourth chapter, we make use of the results in the multi-unit auction literature to study the Balancing Energy Services auctions (electricity spot market auctions) in Texas. We estimate the marginal costs of bidders implied by the Bayesian-Nash equilibrium of the multi-unit auction model of the market. We then compare the estimates to the actual marginal cost data. We find that, for the BES auction we study, the three largest bidders, Luminant, NRG and Calpine, have marked-down their bids more than the optimal amount implied by the model for the quantities where they were short of their contractual obligations, while they have put a mark-up larger than the optimal level implied by the model for quantities in excess of their contract obligations. Among the three bidders we studied, Calpine has come closest to bidding its optimal implied by the Bayesian-Nash equilibrium of the multi-unit auction model of the BES market.
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    Robust GARCH methods and analysis of partial least squares regression
    (2014-04-24) Egbulefu, Joseph; Cox, Dennis D.; Ensor, Katherine B.; El-Gamal, Mahmoud A.
    New approaches to modeling volatility are evaluated and properties of partial least squares (PLS) regression are investigated. Common methods for modeling volatility, the standard deviation of price changes over a period, that account for the heavy tails of asset returns rely on maximum likelihood estimation using a heavy-tailed distribu- tion. A fractional power GARCH model is developed for robust volatility modeling of heavy tailed returns using a fractional power transform and Gaussian quasi maximum likelihood estimation. Furthermore, a smooth periodic GARCH model, incorporating seasonal trends by wavelet analysis, is developed and shown to outperform existing approaches in long-horizon volatility forecasting. PLS is a latent variable method for regression with correlated predictors. Previous approaches to derive the asymptotic covariance of PLS regression coefficients rely on restrictive assumptions. The asymptotic covariance of PLS coefficients are derived under general conditions. PLS regression is applied to variable selection in the context of index tracking.
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    Statistical models for intraday trading dynamics
    (2007) Bhatti, Chad Reyhan; Cox, Dennis D.
    Advances in computational power and data storage have spawned a new research area in financial economics and statistics called high-frequency finance. The defining feature of high-frequency finance is the analysis of financial processes over short intraday time horizons. This time horizon may be the trade-by-trade behavior of the market, or it may be locally aggregated behavior over intraday intervals. The analysis of intraday financial processes is motivated by the micro-foundations of aggregate market behavior. It is hoped that micro-level market properties can help explain macro-level market properties. Two topics of particular interest are the statistical modeling of these intraday processes and the temporal aggregation of these intraday statistical models. This dissertation examines the statistical modeling of intraday trading dynamics. The particular aspect of trading dynamics of interest is the relationship between the trade and quote processes. The affect of trading activity on quoting behavior is one of the central problems in the economic theory of market microstructure. In order to investigate this relationship at the transaction level, the dynamics of the trade and quote processes for eight securities traded on the New York Stock Exchange (NYSE) are modeled in a market microstructure framework. We begin by defining the EL Model and the EL Model framework developed in Engle and Lunde (2003). We propose an alternative to the EL Model for the modeling of trade and quote dynamics using the Cox regression model. The Cox regression model has many data analytic advantages. With the Cox regression model we are able to perform a thorough statistical analysis of transaction level trade and quote behavior. We conclude by investigating a local Poisson approximation of intraday trade and quote behavior in five minute intervals using the Poisson generalized linear model with dispersion.