Robust Estimation of a High-Dimensional Integrated Covariance Matrix

2012 ◽  
Author(s):  
Takayuki Morimoto ◽  
Shuichi Nagata
Keyword(s):  
Covariance Matrix ◽  
Robust Estimation ◽  
High Dimensional ◽  
Integrated Covariance

Pre-averaging estimate of high dimensional integrated covariance matrix with noisy and asynchronous high-frequency data

2018 ◽  
Vol 07 (03) ◽  
pp. 1850005 ◽  
Author(s):  
Zhi Liu ◽  
Xiaochao Xia ◽  
Guoliang Zhou
Keyword(s):  
Covariance Matrix ◽  
High Frequency ◽  
Rapid Development ◽  
Global Market ◽  
High Frequency Data ◽  
High Dimensional ◽  
Frequency Data ◽  
Microstructure Noise ◽  
Matrix Estimation ◽  
Integrated Covariance

With rapid development of the global market, the number of financial securities has significantly grown, which greatly challenges the measuring of financial quantities. Among others, the estimation of covariance matrix which plays an important role in risk management becomes no longer accurate. In this paper, we consider the estimation of integrated covariance matrix of semi-martingales under framework of high dimension by using high frequency data. We assume that the multivariate asset prices are observed asynchronously and all the observed prices are contaminated by microstructure noise. We employ the pre-averaging method to remove the microstructure noise and the generalized synchronization method to deal with the non-synchronicity. Moreover, to avoid the inconsistency in the high-dimensional covariance matrix estimation, we propose a regularized estimate. The consistency under matrix [Formula: see text]-norm is established. Compared to existing results, our estimator improves the accuracy of the estimation. Finally, we assess the theoretical results via some simulation studies.

scholarly journals ON DETERMINING THE NUMBER OF SPIKES IN A HIGH-DIMENSIONAL SPIKED POPULATION MODEL

2012 ◽  
Vol 01 (01) ◽  
pp. 1150002 ◽  
Author(s):  
DAMIEN PASSEMIER ◽  
JIAN-FENG YAO
Keyword(s):  
Covariance Matrix ◽  
Population Model ◽  
Factor Model ◽  
Fundamental Problem ◽  
High Dimensional ◽  
Sample Covariance ◽  
Or Economics ◽  
Linear Mixture Model ◽  
The Difference ◽  
Scientific Fields

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific fields, including signal processing (linear mixture model) or economics (factor model). Several recent papers studied the asymptotic behavior of the eigenvalues of the sample covariance matrix (sample eigenvalues) when the dimension of the observations and the sample size both grow to infinity so that their ratio converges to a positive constant. Using these results, we propose a new estimator based on the difference between two consecutive sample eigenvalues.

scholarly journals On eigenvalues of a high-dimensional spatial-sign covariance matrix

Bernoulli ◽  
2022 ◽  
Vol 28 (1) ◽  
Author(s):  
Weiming Li ◽  
Qinwen Wang ◽  
Jianfeng Yao ◽  
Wang Zhou
Keyword(s):  
Covariance Matrix ◽  
High Dimensional
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