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Keywords:

  • Beta distribution;
  • eBay;
  • Forecasting;
  • Functional data;
  • Growth models;
  • Kullback–Leibler distance;
  • Price path;
  • Price velocity

Summary.  The path that the price takes during an on-line auction plays an important role in understanding and forecasting on-line auctions. Price dynamics, such as the price velocity or its acceleration, capture the speed at which auction information changes. The ability to estimate price dynamics accurately is especially important in realtime price forecasting, where bidders and sellers must make quick decisions or react to changes in market conditions. Existing models for estimating price paths from observed bid data suffer from issues of non-monotonicity, high variability or computational inefficiency. We propose a flexible two-parameter beta model which adequately captures a wide range of auction price paths. The model is computationally efficient and has several properties that make it especially advantageous in the on-line auction context. We compare the beta model with non-parametric and parametric alternatives empirically, when used in a variety of forecasting models. Using bidding data from eBay auctions, we find that the beta model leads to fast and high accuracy price predictions. This behaviour is consistent across various forecasting models and data sets. The implication for practice is the usefulness of the beta model for obtaining accurate and realtime bidding and selling decisions in on-line markets.