Forecasting High-Dimensional Financial Functional Time Series: An Application to Constituent Stocks in Dow Jones Index

Abstract

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.