Forecasting Intraday S&P 500 Index Returns: A Functional Time Series Approach

Abstract

Financial data often take the form of a collection of curves observed sequentially over time. Example of which include intraday stock price curves and intraday volatility curves. These curves can be viewed as a time series of functions observed at an equally spaced and dense grid. The nature of high-dimensional data poses challenges from a statistical aspect due to the so-called curse of dimensionality, but it also poses opportunities to analyse a rich source of information for better understanding dynamic changes at a short time interval. In this paper, we consider forecasting a time series of functions and put forward some statistical methods to forecast one-day-ahead intraday stock return; as we sequentially observe new data, we also consider the issue of dynamic updating to update point and interval forecasts for achieving better accuracy. These forecasting methods are validated through an empirical study of five-minute intraday S&P 500 index returns.

Keywords: dynamic updating, functional principal component regression, functional linear regression, ordinary least squares, penalise least squares, ridge regression

JEL Classification: C14, C55, G12, G17