Annals of Applied Statistics

The BARISTA: A model for bid arrivals in online auctions

Galit Shmueli, Ralph P. Russo, and Wolfgang Jank

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The arrival process of bidders and bids in online auctions is important for studying and modeling supply and demand in the online marketplace. A popular assumption in the online auction literature is that a Poisson bidder arrival process is a reasonable approximation. This approximation underlies theoretical derivations, statistical models and simulations used in field studies. However, when it comes to the bid arrivals, empirical research has shown that the process is far from Poisson, with early bidding and last-moment bids taking place. An additional feature that has been reported by various authors is an apparent self-similarity in the bid 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 arrivals and accounts for these features. The goal of this paper is to introduce a family of distributions that well-approximate the bid time distribution in hard-close auctions. We call this the BARISTA process (Bid ARrivals In STAges) because of its ability to generate different intensities at different stages. 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 Finally, we show how a Poisson bidder arrival process relates to a BARISTA bid arrival process.

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Ann. Appl. Stat., Volume 1, Number 2 (2007), 412-441.

First available in Project Euclid: 30 November 2007

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Nonhomogenous Poisson process bidding frequency self-similarity bidding dynamics sniping


Shmueli, Galit; Russo, Ralph P.; Jank, Wolfgang. The BARISTA: A model for bid arrivals in online auctions. Ann. Appl. Stat. 1 (2007), no. 2, 412--441. doi:10.1214/07-AOAS117.

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