Feature Extraction for Functional Time Series: Theory and Application to NIR Spectroscopy Data

TL;DR

This paper introduces FPCA-BTW, a new method combining global FPCA and local wavelet thresholding to extract comprehensive features from functional time series, improving analysis and forecasting accuracy.

Contribution

The paper presents a novel FPCA-BTW approach that simultaneously captures global and local features in functional time series, addressing limitations of traditional FPCA.

Findings

FPCA-BTW outperforms FPCA and sparse FPCA in simulations.

Local features improve forecasting accuracy.

Asymptotic properties of estimators are established.

Abstract

We propose a novel method 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 local features of function variations over particular short intervals within function domain, are both important in functional data analysis. Functional principal component analysis (FPCA), though a key feature extraction tool, only focus on capturing the dominant global features, neglecting highly localized features. We introduce a 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 FPCA in 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.