  Intraday financial data often take the form of a collection of curves that
can be observed sequentially over time, such as intraday stock price curves.
These curves can be viewed as a time series of functions observed on equally
spaced and dense grids. Due to the curse of dimensionality, high-dimensional
data poses challenges from a statistical aspect; however, it also provides
opportunities to analyze a rich source of information so that the dynamic
changes within short-time intervals can be better understood. We consider a
sieve bootstrap method of Paparoditis and Shang (2022) to construct
one-day-ahead point and interval forecasts in a model-free way. As we
sequentially observe new data, we also implement two dynamic updating methods
to update point and interval forecasts for achieving improved accuracy. The
forecasting methods are validated through an empirical study of 5-minute
cumulative intraday returns of the S&P/ASX All Ordinaries Index.
