Exploring and Modeling Online Auctions Using Functional Data Analysis

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In recent years, the increasing popularity of eCommerce, and particularly online auctions has stirred a great amount of scholarly research, especially in information systems, economics, and marketing, but little or no attention has been received from statistics. ECommerce arrives with enormous amounts of rich and clean data as well as statistical challenges. eCommerce not only creates new data challenges, it also motivates the need for innovative models. While there exist many theories about economic behavior of participants in market exchanges, many of these theories have been developed before the appearance of the world wide web and often are not appropriate to be used in explaining modern economic behavior in eCommerce. This calls for new models that describe not only the evolution of a process, but also its dynamics. This research takes a different look at online auctions and proposes to study an auction's price evolution and associated price dynamics from different points of view using functional data analysis techniques.

In this dissertation, we develop novel dynamic modeling procedures applicable to online auctions. First, we develop a dynamic forecasting system to predict the price of an ongoing auction. By dynamic we mean that the model can predict the price of an auction ``in-progress" and can update its prediction based on newly arriving information. Our dynamic forecasting model accounts for the special features of online auction data by using modern functional data analysis techniques. We also use the functional context to systematically describe the empirical regularities of auction dynamics. Second, we propose a family of differential equation models to capture the dynamics in online auctions. A novel multiple comparisons test is proposed to compare dynamics models of auction sub-populations. We accomplish the modeling task within the framework of principal differential analysis and functional models. Third, we propose Model-based Functional Differential Equation Trees to better incorporate the different characteristics of the auction, item, bidders and seller into the differential equation. We compare this new tree-method with trees either based on high-dimensional multivariate responses or functional responses. We apply our methods to a novel set of Harry Potter and Microsoft Xbox data for model validation and comparison of method.