Functional Principal Component Analysis of Cointegrated Functional Time Series

Abstract

Functional principal component analysis (FPCA) has played an important role in the development of functional time series (FTS) analysis. This paper investigates how FPCA can be used to analyze cointegrated functional time series and propose 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 KPSS-type tests for examining some essential properties of cointegrated time series. As an empirical illustration, our methodology is applied to the time series of log-earning densities.* I am grateful to Brendan Beare and Morten Nielsen for helpful comments on an early draft of this paper. Data and R code to replicate simulation and empirical results are available on the author's website.

Cointegration and Representation of Cointegrated Autoregressive Processes in Banach Spaces

“…They therefore employed the sup-distance, which is expected to better reflect the visualization of curve-valued observations in statistical analysis, by assuming that such observations are random elements of C [0,1]. In this regard, nonstationary, and possibly cointegrated, time series considered in the L 2 [0,1] setting can be potentially reconsidered in a Banach space setting; as an example of such time series, curves of age-specific employment rates (Nielsen et al, 2019;Seo, 2020), population counts (Shang et al, 2016), mortality rates (Gao and Shang, 2017), or fertility rates (Hyndman and Ullah, 2007) can be mentioned.…”