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.

Time-series forecasting has a large number of applications. Users with a partial time series for auctions, new stock offerings, or industrial processes desire estimates of the future behavior. We present a data driven forecasting method and interface called similarity-based forecasting (SBF). A pattern matching search in an historical time series dataset produces a subset of curves similar to the partial time series. The forecast is displayed graphically as a river plot showing statistical information about the SBF subset. A forecasting preview interface allows users to interactively explore alternative pattern matching parameters and see multiple forecasts simultaneously. User testing with 8 users demonstrated advantages and led to improvements.

We propose a dynamic model for forecasting price in online auctions. One of the key features of our model is that it operates during the live-auction, which makes it different from previous approaches that only consider static models. Our model is also different with respect to how information about price is incorporated. While one part of the model is based on the more traditional notion of an auction's price-level, another part incorporates its dynamics in the form of a price's velocity and acceleration. In that sense, it incorporates key features of a dynamic environment such as an online auction. The use of novel functional data methodology allows us to measure, and subsequently include, dynamic price characteristics. We illustrate our model on a diverse set of eBay auctions across many different book categories. We find significantly higher prediction accuracy compared to standard approaches.

The reliability of consecutive-type systems has been approached from various angles. A new method is presented for deriving exact expressions for the generating functions and the reliabilities of various consecutive-type systems. This method, based on Feller's run theory, is easy to implement, and leads to both recursive and nonrecursive formulas for the reliability. The nonrecursive expression is especially advantageous for systems with numerous components. In comparison to the n (number of components) computations that the recursive formulas require, the nonrecursive formula only requires the computation of the roots of a polynomial of order k. The method is extended for computing generating functions and reliabilities of systems with multi-state components as well as systems with s-dependent components.