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.
Highlights
IntroductionRecent advances in data collection and storage have enabled people to access data with increasing dimensions and volumes
Recent advances in data collection and storage have enabled people to access data with increasing dimensions and volumes. These densely or ultradensely observed data can be modeled under a functional data analysis (FDA) framework, assuming the observations are recorded at discretized grid points of a random smooth curve
This has led to the development of two strands of statistics—high-dimensional data analysis and FDA
Summary
Recent advances in data collection and storage have enabled people to access data with increasing dimensions and volumes These densely or ultradensely observed data can be modeled under a functional data analysis (FDA) framework, assuming the observations are recorded at discretized grid points of a random smooth curve. This is especially useful for finance research, where the data are recorded at a very high frequency or even, almost continuously. For densely observed functional data, the observations are often presmoothed so that they are assumed to be drawn from the smoothed trajectories (Cardot 2000; Zhang and Chen 2007; Zhang and Wang 2016) To some degree, this smoothness assumption converts the “curse” to the “blessing” of dimensionality, as one can pool information from neighboring grid points to overcome the high-dimensional problem. Panaretos and Tavakoli (2013), Hörmann et al (2015), Rice and
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