Modeling eBay price using stochastic differential equations

Online auctions have become increasingly popular in recent years. There is a growing body of research on this topic, whereas modeling online auction price curves constitutes one of the most interesting problems. Most research treats price curves as deterministic functions, which ignores the random effects of external and internal factors. To account for the randomness, a more realistic model using stochastic differential equations is proposed in this paper. The online auction price is modeled by a stochastic differential equation in which the deterministic part is equivalent to the second-order differential equation model proposed in Wang et al. (Journal of the American Statistical Association, 2008, 103, 1100-1118). The model also includes a component representing the measurement errors. Explicit expressions for the likelihood function are also obtained, from which statistical inference can be conducted. Forecast accuracy of the proposed model is compared with the ODE (ordinary differential equation) approach. Simulation results show that the proposed model performs better.