  We develop theory leading to testing procedures for the presence of a change
point in the intraday volatility pattern. The new theory is developed in the
framework of Functional Data Analysis. It is based on a model akin to the
stochastic volatility model for scalar point-to-point returns. In our context,
we study intraday curves, one curve per trading day. After postulating a
suitable model for such functional data, we present three tests focusing,
respectively, on changes in the shape, the magnitude and arbitrary changes in
the sequences of the curves of interest. We justify the respective procedures
by showing that they have asymptotically correct size and by deriving
consistency rates for all tests. These rates involve the sample size (the
number of trading days) and the grid size (the number of observations per day).
We also derive the corresponding change point estimators and their consistency
rates. All procedures are additionally validated by a simulation study and an
application to US stocks.
