Functional Principal Component Analysis for Cointegrated Functional Time Series

TL;DR

This paper introduces a modified functional principal component analysis (FPCA) tailored for cointegrated functional time series, enhancing estimation efficiency and enabling new testing methods for key properties.

Contribution

The paper proposes a novel modification of FPCA that improves estimation of cointegrating vectors and introduces FPCA-based tests for cointegration properties.

Findings

Modified FPCA yields more efficient estimators.

New tests for cointegration properties are developed.

The approach advances analysis of cointegrated functional time series.

Abstract

Functional principal component analysis (FPCA) has played an important role in the development of functional time series analysis. This note investigates how FPCA can be used to analyze cointegrated functional time series and proposes a modification of FPCA as a novel statistical tool. Our modified FPCA not only provides an asymptotically more efficient estimator of the cointegrating vectors, but also leads to novel FPCA-based tests for examining essential properties of cointegrated functional time series.