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.

翻译：日内金融数据通常表现为一系列可随时间顺序观测的曲线集合，例如日内股票价格曲线。这些曲线可被视为在等距密集网格上观测到的函数时间序列。由于维数诅咒，高维数据从统计角度带来挑战；然而，这同时也提供了分析丰富信息源的机遇，从而能更深入地理解短时间间隔内的动态变化。我们采用Paparoditis和Shang（2022）提出的筛子自助法，以无模型方式构建次日逐点预测和区间预测。随着新数据的顺序观测，我们还实施两种动态更新方法，通过更新逐点预测和区间预测来提高预测精度。通过对S&P/ASX全普通股指数5分钟累计日内收益率的实证研究，验证了这些预测方法的有效性。