Title: Time deformation return model

In the talk, we present a time deformation return model for the return process or the series of differences of two adjacent log-prices of a stock. In particular, the trading duration process is used as the directing process to deform the calendar time. For this model, we develop a procedure based on the method of generalized moments for parameter estimation, in which the number of moments is chosen through simulations. We illustrate the proposed model and inferential procedure by an analysis of IBM stock data.