Title: Feature extraction for functional time series: Theory and application to NIR spectroscopy data
Authors: Yang Yang - Monash University (Australia) [presenting]
Han Lin Shang - Macquarie University (Australia)
Yanrong Yang - The Australian National University (Australia)
Abstract: A novel method is proposed to extract global and local features of functional time series. The global features concerning the dominant modes of variation over the entire function domain, and the local features of function variations over particular short intervals within the function domain, are both important in functional data analysis. Functional principal component analysis (FPCA), though a key feature extraction tool, only focuses on capturing the dominant global features, neglecting highly localized features. We introduce an FPCA-BTW method that initially extracts global features of functional data via FPCA, and then extracts local features by block thresholding of wavelet (BTW) coefficients. Using Monte Carlo simulations, along with an empirical application on near-infrared spectroscopy data of wood panels, we illustrate that the proposed method outperforms competing methods, including FPCA and sparse FPCAin the estimation functional processes. Moreover, extracted local features inheriting serial dependence of the original functional time series contribute to more accurate forecasts. Finally, we develop asymptotic properties of FPCA-BTW estimators, discovering the interaction between convergence rates of global and local features.