Online auctions have become increasingly popular in recent years, and as a consequence there is a growing body of empirical research on this topic. Most of that research treats data from online auctions as cross-sectional, and consequently ignores the changing dynamics that occur during an auction. In this article we take a different look at online auctions and propose to study an auction's price evolution and associated price dynamics. Specifically, 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. Forecasting price in online auctions is challenging because traditional forecasting methods cannot adequately account for two features of online auction data: (1) the unequal spacing of bids and (2) the changing dynamics of price and bidding throughout the auction. Our dynamic forecasting model accounts for these special features by using modern functional data analysis techniques. Specifically, we estimate an auction's price velocity and acceleration and use these dynamics, together with other auction-related information, to develop a dynamic functional forecasting model. We also use the functional context to systematically describe the empirical regularities of auction dynamics. We apply our method to a novel set of Harry Potter and Microsoft Xbox data and show that our forecasting model outperforms traditional methods.
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