The BARISTA: A Model For Bid Arrivals in Online Auctions

The arrival process of bidders and bids in online auctions is important for studying and modelling supply and demand in the online marketplace. A popular assumption in the online auction literature is that a Poisson process is a reasonable approximation. This approximation underlies theoretical derivations, statistical models and simulations used in field studies. However, there has been much evidence that the arrival of bids (or bidders) is affected by deadline and earliness effects. This leads to a three-stage process that is not captured by the homogenous Poisson model. An additional feature that has been reported by various authors is an apparent self-similarity in the arrival process. Despite the wide evidence for the changing bidding intensities and the self-similarity, there has been no rigorous attempt at developing a model that adequately approximates bid data. In this paper we introduce a non-homogeneous Poisson process that captures these features. We call this the BARISTA process (Bid ARrivals In STAges) because of its ability to generate different intensities at different stages, like espresso drinks with different intensities. We describe the properties of this model, show how to simulate bid arrivals from it, and how to use it for estimation and inference. We illustrate its power and usefulness by fitting simulated and real data from eBay.com.