The wide availability of high-frequency data for many financial instruments stimulates a upsurge interest in statistical research on the estimation of volatility. Jump-diffusion processes observed with market microstructure noise are frequently used to model high-frequency financial data. Yet,...

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to infinity as the sample size n increases. Motivated by the Arbitrage Pricing Theory in finance, a...

We develop a specification test for discretely-sampled jump-diffusions, based on a comparison of a nonparametric estimate of the transition density or distribution function to their corresponding parametric counterparts. As a special case, our method applies to pure diffusions. We propose three...

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when the covariates are highly correlated. Motivated by...

The constant elasticity of substitution (CES) function is an important function that is widely used in both theoretical analysis and applied economics. We propose a systematic framework to estimate the deep nested CES function using the nonlinear least squares (NLS) method. This method fills the...

Event studies of market efficiency measure an earnings surprise with the consensus error (CE), defined as earnings minus the average of professional forecasts. If a subset of forecasts can be biased, the ideal but difficult to estimate parameter-dependent alternative to CE is a nonlinear filter...

Recently several large volatility matrix estimation procedures have been developed for factor-based Ito processes whose integrated volatility matrix consists of low-rank and sparse matrices. Their performance depends on the accuracy of input volatility matrix estimators. When estimating...

Several novel large volatility matrix estimation methods have been developed based on the high-frequency financial data. They often employ the approximate factor model that leads to a low-rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large...

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...

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...