Statistics and Its Interface

Volume 11 (2018)

Number 2

Determining the number of factors for high-dimensional time series

Pages: 307 – 316

DOI: https://dx.doi.org/10.4310/SII.2018.v11.n2.a8

Authors

Qiang Xia (College of Mathematics and Informatics, South China Agricultural University, Guangzhou, China)

Rubing Liang (College of Mathematics and Informatics, South China Agricultural University, Guangzhou, China)

Jianhong Wu (School of Mathematics and Science, Shanghai Normal University, Shanghai, China)

Heung Wong (Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong)

Abstract

In this paper, we suggest a new method of determining the number of factors in factor modeling for high-dimensional stationary time series. When the factors are of different degree of strength, the eigenvalue-based ratio method of Lam and Yao needs a two-step procedure to estimate the number of factors. As a modification of the method, however, our method only needs a one-step procedure for the determination of the number of factors. The resulted estimator is obtained simply by minimizing the ratio of the contribution of two adjacent eigenvalues. Some asymptotic results are also developed for the proposed method. The finite sample performance of the method is well examined and compared with some competitors in the existing literature by Monte Carlo simulations and a real data analysis.

Keywords

autocovariance matrices, contribution ratio, eigenvalues, factor models, number of factors

2010 Mathematics Subject Classification

Primary 60E99, 62H25. Secondary 91B84.

Full Text (PDF format)

The work of Qiang Xia was partially supported by the Ministry of Education in China Project of Humanities and Social Sciences (No. 17YJA910002), by the National statistical plan for scientific research project of China (No. 2015LZ48), and by the Major Research Plan of the National Natural Science Foundation of China (No. 91746102).

The work of Rubing Liang was partially supported by the National Science Foundation of Guangdong Province of China (No. 2015A030310365) and (No. 2016A030313414), and by the Research Committee of The Hong Kong Polytechnic University (G-YBCV).

The work of Jianhong Wu was partially supported by the National Science Foundation of China (No. 11671263).

The work of Heung Wong was partially supported by the Research Committee of The Hong Kong Polytechnic University (G-YBCV).

Received 21 December 2016

Published 7 March 2018