Dynamic principal component analysis with missing values

Junhyeon Kwon; Hee-Seok Oh; Yaeji Lim

doi:10.1080/02664763.2019.1699910

Dynamic principal component analysis with missing values

J Appl Stat. 2019 Dec 8;47(11):1957-1969. doi: 10.1080/02664763.2019.1699910. eCollection 2020.

Authors

Junhyeon Kwon¹, Hee-Seok Oh¹, Yaeji Lim²

Affiliations

¹ Department of Statistics, Seoul National University, Seoul, Korea.
² Department of Applied Statistics, Chung-Ang University, Seoul, Korea.

Abstract

Dynamic principal component analysis (DPCA), also known as frequency domain principal component analysis, has been developed by Brillinger [Time Series: Data Analysis and Theory, Vol. 36, SIAM, 1981] to decompose multivariate time-series data into a few principal component series. A primary advantage of DPCA is its capability of extracting essential components from the data by reflecting the serial dependence of them. It is also used to estimate the common component in a dynamic factor model, which is frequently used in econometrics. However, its beneficial property cannot be utilized when missing values are present, which should not be simply ignored when estimating the spectral density matrix in the DPCA procedure. Based on a novel combination of conventional DPCA and self-consistency concept, we propose a DPCA method when missing values are present. We demonstrate the advantage of the proposed method over some existing imputation methods through the Monte Carlo experiments and real data analysis.

Keywords: Dynamic principal component analysis; dynamic factor model; frequency domain principal component analysis; missing problem; spectral density matrix.

Grants and funding

This research was supported by the Seoul National University Research Grant in 2018 and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korea government (NRF-2018R1D1A1B07042933, NRF-2019R1A2C4069453).