A family of growth models for representing the price process in online auctions

Abstract

Bids during an online auction arrive at unequally-spaced discrete time points. Our goal is to capture the entire continuous price-evolution function by representing it as a functional object. Various nonparametric smoothing methods exist to recover the functional object from the observed discrete bid data. Previous studies use penalized polynomial and monotone smoothing splines; however, these require the determination and storage of a large number of coefficients and often lengthy computational time. We present a family of parametric growth curves that describe the price-evolution during online auctions. This approach is parsimonious and has an appealing interpretation in the online auction context. We also provide an automated fitting algorithm that is computationally fast. Methods are illustrated using eBay data.