On the Inference of the Spikes for the High-Dimensional Covariance Matrix Based on High-Frequency Data

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Keren Shen* and JIANFENG YAO and Wai Keung Li
• Companies: and The University of Hong Kong and The University of Hong Kong
• Keywords: high-dimensional ; pre-averaging ; spiked model ; high-frequency ; realized covariance matrix

Abstract

Recently, Xia and Zheng (2015a) consider the inference of the spectrum of the high-dimensional integrated covariance matrix (ICV) based on the high-frequency data. They propose a version of pre-averaging estimator whose limiting spectral distribution depends only on that of the ICV through the Marcenko-Pastur equation. However, there always exist some spikes for the realized covariance matrix for the real data which are not dealt with by the model of Xia and Zheng (2015a). We propose a generalized spiked model which constructs a link between the spikes of the ICV and those of the pre-averaging estimator. As a result, the spikes of the ICV can be inferred which is useful in many applications such as portfolio management. Asymptotic consistency is demonstrated by extensive simulation studies. In addition, we apply our model to the real data in the US market and the Hong Kong market. Our model provides a theoretical support for the "bulk + spikes" structure of the pre-averaging covariance matrix. It is found that our model outperforms the existing one, both from the empirical and statistical view.