Financial data (e.g., intraday share prices) are recorded almost continuously and thus take the form of a series of curves over the trading days. Those sequentially collected curves can be viewed as functional time series. When we have a large number of highly correlated shares, their intraday prices can be viewed as high-dimensional functional time series (HDFTS). In this paper, we propose a new approach to forecasting multiple financial functional time series that are highly correlated. The difficulty of forecasting high-dimensional functional time series lies in the “curse of dimensionality.” What complicates this problem is modeling the autocorrelation in the price curves and the comovement of multiple share prices simultaneously. To address these issues, we apply a matrix factor model to reduce the dimension. The matrix structure is maintained, as information contains in rows and columns of a matrix are interrelated. An application to the constituent stocks in the Dow Jones index shows that our approach can improve both dimension reduction and forecasting results when compared with various existing methods.

中文翻译：

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预测高维金融函数时间序列：对道琼斯指数成分股的应用

财务数据（例如，日内股价）几乎是连续记录的，因此在交易日内采用一系列曲线的形式。那些按顺序收集的曲线可以看作是函数时间序列。当我们拥有大量高度相关的股票时，它们的日内价格可以被视为高维函数时间序列（HDFTS）。在本文中，我们提出了一种预测多个高度相关的金融功能时间序列的新方法。预测高维函数时间序列的难点在于“维数诅咒”。使这个问题复杂化的是同时对价格曲线中的自相关和多个股票价格的联动进行建模。为了解决这些问题，我们应用矩阵因子模型来降低维度。矩阵结构保持不变，因为矩阵的行和列中包含的信息是相互关联的。对道琼斯指数成分股的应用表明，与各种现有方法相比，我们的方法可以改善降维和预测结果。