  Heteroskedasticity is a common feature of financial time series and is
commonly addressed in the model building process through the use of ARCH and
GARCH processes. More recently multivariate variants of these processes have
been in the focus of research with attention given to methods seeking an
efficient and economic estimation of a large number of model parameters. Due to
the need for estimation of many parameters, however, these models may not be
suitable for modeling now prevalent high-frequency volatility data. One
potentially useful way to bypass these issues is to take a functional approach.
In this paper, theory is developed for a new functional version of the
generalized autoregressive conditionally heteroskedastic process, termed
fGARCH. The main results are concerned with the structure of the fGARCH(1,1)
process, providing criteria for the existence of a strictly stationary
solutions both in the space of square-integrable and continuous functions. An
estimation procedure is introduced and its consistency verified. A small
empirical study highlights potential applications to intraday volatility
estimation.
