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Title: Identifying features from practical FPCA on functional time series Authors:  Yuan Gao - The Australian National University (Australia) [presenting]
Yanrong Yang - The Australian National University (Australia)
Han Lin Shang - Australian National University (Australia)
Yang Yang - University of Newcastle (Australia)
Abstract: As a typical dimension-reduction tool, functional principal component analysis (FPCA) extracts features for functional data in terms of the sample covariance operator. What kind of features does FPCA produce? Under a general separable covariance structure, we show that this set of FPCA features may include principal components of the population covariance structure (i.e., cross-sectional common variation), basis functions of the nonstationary subspace (i.e. temporal common movement), and their mixture. We provide asymptotic results for the sub-space expanded by these features. We also construct an alternative algorithm to differentiate the two kinds of features and demonstrate this by applying it to the U.S. mortality rates and the global temperature data.