Modeling the Distribution of Financial Returns by Functional Data Analysis

In this paper, we use functional data analysis to model a time varying unconditional distribution of financial intraday returns. This is in the spirit of the recent development of realized volatility modeling (e.g. Andersen et al, 2001), where one of the moments of this uncondional distribution, the realized volatility, is assumed to change smoothly over time. In the approach used in this paper, we instead assume that the entire distribution function changes smoothly over time. This enable us to study autoand cross dependencies of different parts of the unconditional distribion with no model assumptions but the smoothness of the distribution function. We develop a simulation based procedure for statistical inference of the model. Finally, we apply the method to the Swiss Franc-US Dollar exchange rate 1985-1991.