Statistics Across Campuses: Yanrong Yang -- Can we trust PCA on non-stationary Data?

Can we trust PCA on non-stationary Data? 

Date: 13 August 2020, Thursday 

Time: 10am 

Speaker: Dr Yanrong Yang (ANU) 

Abstract: 

This paper establishes asymptotic properties for spiked empirical eigenvalues for high
dimensional data with both cross-sectional dependence and dependent sample structure.  A
new finding from the established theoretical results is that spiked empirical
eigenvalues will reflect dependent sample structure instead of cross-sectional structure
under some scenarios, which indicates that principal component analysis (PCA) may
provide inaccurate inference for cross-sectional structure.  An illustrated example is
provided to show that some commonly used statistics based on spiked empirical
eigenvalues mis-estimate the true number of common factors.  As an application on high
dimensional time series, we propose a test statistic to distinguish unit root from
factor structure, and demonstrate its effective finite sample performance on simulated
data.  Our results are then applied to analyse OECD health care expenditure data and US
mortality data, both of which possess cross-sectional dependence as well as
non-stationary temporal dependence.  It is worth mentioning that we contribute to
statistical justification for the benchmark paper by Lee and Carter (1992) in mortality
forecasting.  

Link: https://anu.zoom.us/j/425258947