Covariance between Stochastic Processes Observed Sparsely with Noise: Application to Online Auctions

Abstract:     
Integrated covariance between pairs of realizations of a multivariate Ito process observed sparsely and irregularly with additive noise is estimated using the random lead lag estimator. The method is applied to a dataset of price processes from online auctions on ebay. This approach allows us to study how the covariance between pairs of auctions depends on covariates given by the times and lengths of auctions. Principal components analysis of the covariance matrix of auctions can achieve substantial data reduction and provide valuable insights on the interdependence of the price trajectories of online auctions.

Keywords: Multivariate Ito process, Asynchronicity, Principal Components Analysis, Online Auctions, Integrated covariance

working papers series