Forecasting intraday S&P 500 index returns: A functional time series approach

Financial data often take the form of a collection of curves that can be observed sequentially over time; for example, intraday stock price curves and intraday volatility curves. These curves can be viewed as a time series of functions that can be observed on equally spaced and dense grids. Owing to the so‐called curse of dimensionality, the nature of high‐dimensional data poses challenges from a statistical perspective; however, it also provides opportunities to analyze a rich source of information, so that the dynamic changes of short time intervals can be better understood. In this paper, we consider forecasting a time series of functions and propose a number of statistical methods that can be used to forecast 1‐day‐ahead intraday stock returns. As we sequentially observe new data, we also consider the use of dynamic updating in updating point and interval forecasts for achieving improved accuracy. The forecasting methods were validated through an empirical study of 5‐minute intraday S&P 500 index returns.