Dynamically integrated regression model for online auction data

We propose a dynamically integrated regression model to predict the price of online auctions,including the final price.Different from existing models,the proposed method uses not only the historical price but also the information from bidding time.Consequently,the prediction accuracy is improved compared with the existing methods.An estimation method based on B-spline approximation is proposed for the estimation and the inference of parameters and nonparametric functions in this model.The minimax rate of convergence for the prediction risk and large-sample results including the consistency and the asymptotic normality are established.Simulation studies verify the finite sample performance and the appealing prediction accuracy and robustness.Finally,when we apply our method to a 7-day auction of iPhone 6s during December 2015 and March 2016,the proposed method predicts the ending price with a much smaller error than the existing models.