High-frequency financial data allow us to estimate large volatility matrices with relatively short time horizon. Many novel statistical methods have been introduced to address large volatility matrix estimation problems from a high-dimensional Ito process with microstructural noise...

We document a striking block-diagonal pattern in the factor model residual covariances of the S&P 500 Equity Index constituents, after sorting the assets by their assigned Global Industry Classification Standard (GICS) codes. Cognizant of this structure, we propose combining a location-based...

We propose a bootstrap-based robust high-confidence level upper bound (Robust H-CLUB) for assessing the risks of large portfolios. The proposed approach exploits rank-based and quantile-based estimators, and can be viewed as a robust extension of the H-CLUB method (Fan et al., 2015). Such an...

This paper examines the leverage effect, or the generally negative covariation between asset returns and their changes in volatility, under a general setup that allows the log-price and volatility processes to be Ito semimartingales. We decompose the leverage effect into continuous and...

An aggregated method of nonparametric estimators based on time-domain and state-domain estimators is proposed and studied. To attenuate the curse of dimensionality, we propose a factor modeling strategy. We first investigate the asymptotic behavior of nonparametric estimators of the volatility...

Markowitz (1952, 1959) laid down the ground-breaking work on the mean-variance analysis. Under his framework, the theoretical optimal allocation vector can be very different from the estimated one for large portfolios due to the intrinsic difficulty of estimating a vast covariance matrix and...

We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test statistic in A\quot;{i}t-Sahalia and Jacod (2007), our new test statistic enjoys the same asymptotic properties but has smaller variance. These results...

This paper provides a selective overview on the recent development of factor models and their applications in econometric learning. We focus on the perspective of the low-rank structure of factor models, and particularly draws attentions to estimating the model from the low-rank recovery point...

This paper proposes a consistent and efficient estimator of the high frequency covariance (quadratic covariation) of two arbitrary assets, observed asynchronously with market microstructure noise. This estimator is built upon the marriage of the quasi-maximum likelihood estimator of the...

We propose a novel technique to boost the power of testing a high-dimensional vector $H:\theta=0$ against sparse alternatives where the null hypothesis is violated only by a couple of components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due...