On a spiked model for large volatility matrix estimation from noisy high-frequency data

Keren SHEN, Jianfeng YAO, Wai Keung LI

Research output: Contribution to journalArticles

1 Citation (Scopus)

Abstract

Recently, inference about high-dimensional integrated covariance matrices (ICVs) based on noisy high-frequency data has emerged as a challenging problem. In the literature, a pre-averaging estimator (PA-RCov) is proposed to deal with the microstructure noise. Using the large-dimensional random matrix theory, it has been established that the eigenvalue distribution of the PA-RCov matrix is intimately linked to that of the ICV through the Marčenko–Pasturequation. Consequently, the spectrum of the ICV can be inferred from that of the PA-RCov. However, extensive data analyses demonstrate that the spectrum of the PA-RCov is spiked, that is, a few large eigenvalues (spikes) stay away from the others which form a rather continuous distribution with a density function (bulk). Therefore, any inference on the ICVs must take into account this spiked structure. As a methodological contribution, a spiked model is proposed for the ICVs where spikes can be inferred from those of the available PA-RCov matrices. The consistency of the inference procedure is established. In addition, the methodology is applied to the real data from the US and Hong Kong markets. It is found that the model clearly outperforms the existing one in predicting the existence of spikes and in mimicking the empirical PA-RCov matrices. Copyright © 2018 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)207-221
JournalComputational Statistics and Data Analysis
Volume131
Early online dateJul 2018
DOIs
Publication statusPublished - Mar 2019

Citation

Shen, K., Yao, J., & Li, W. K. (2019). On a spiked model for large volatility matrix estimation from noisy high-frequency data. Computational Statistics and Data Analysis, 131, 207-221. doi: 10.1016/j.csda.2018.06.004

Keywords

  • Integrated covariance matrix
  • Pre-averaging
  • Random matrix theory
  • Spiked covariance matrix

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