Forecasting intraday financial time series with sieve bootstrapping and dynamic updating

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 pose 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 to construct 1-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-min cumulative intraday returns of the S&P/ASX All Ordinaries Index.