Forecasting Online Auctions via Self-Exciting Point Processes

Modeling online auction prices is a popular research topic among statisticians and marketing analysts. Recent research mainly focuses on two directions: one is the functional data analysis (FDA) approach, in which the price–time relationship is modeled by a smooth curve, and the other is the point process approach, which directly models the arrival process of bidders and bids. In this paper, a novel model for the bid arrival process using a self‐exciting point process (SEPP) is proposed and applied to forecast auction prices. The FDA and point process approaches are linked together by using functional data analysis technique to describe the intensity of the bid arrival point process. Using the SEPP to model the bid arrival process, many stylized facts in online auction data can be captured. We also develop a simulation‐based forecasting procedure using the estimated SEPP intensity and historical bidding increment. In particular, prediction interval for the terminal price of merchandise can be constructed. Applications to eBay auction data of Harry Potter books and Microsoft Xbox show that the SEPP model provides more accurate and more informative forecasting results than traditional methods.