Discrepancy Between Global and Local Principal Component Analysis on Large-Panel High-Frequency Data

In this article, we study the discrepancy between the global principal component analysis (GPCA) and local principal component analysis (LPCA) in recovering the common components of a large-panel high-frequency data. We measure the discrepancy by the total sum of squared differences between common components reconstructed from GPCA and LPCA. The asymptotic distribution of the discrepancy measure is provided when the factor space is time invariant as the dimension <i>p</i> and sample size <i>n</i> tend to infinity simultaneously. Alternatively when the factor space changes, the discrepancy measure explodes under some mild signal condition on the magnitude of time-variation of the factor space. We apply the theory to test the invariance in time of the factor space. The test performs well in controlling the Type I error and detecting time-varying factor spaces. This is checked by extensive simulation studies. A real data analysis provides strong evidences that the factor space is always time-varying within a time span longer than one week.