  Improvements in data acquisition and processing techniques have lead to an
almost continuous flow of information for financial data. High resolution tick
data are available and can be quite conveniently described by a continuous time
process. It is therefore natural to ask for possible extensions of financial
time series models to a functional setup. In this paper we propose a functional
version of the popular ARCH model. We will establish conditions for the
existence of a strictly stationary solution, derive weak dependence and moment
conditions, show consistency of the estimators and perform a small empirical
study demonstrating how our model matches with real data.
