Research

Job Market Paper

“Estimating a Large Covariance Matrix in Time-varying Factor Models”

Abstract: This paper deals with the time-varying high-dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based factor model, respectively. The models allow the factor loadings and error covariance matrix to change smoothly over time. We study the rate of convergence of each estimator. Our simulation and empirical study indicate that time-varying covariance matrix estimators generally perform better than time-invariant covariance matrix estimators. Also, if characteristics are available that genuinely explain true loadings, the characteristics can be used to estimate loadings more precisely in finite samples; their helpfulness increases when loadings rapidly change.

Keywords: Time-varying factor models, Characteristic-based factor models, Approximate factor model, High-dimensionality, Local principal component, Thresholding

Job Market Paper Presentation (7minutes)

Manuscripts under Preparation

“Large Covariance Matrix Estimation with Missing Observations and Covariates”

Abstract: This paper introduces a covariance matrix estimator using a semi-parametric factor model from high-dimensional panel data with missing observations. We first estimate the projected data matrix onto a given linear space spanned by covariates by applying the propensity score to partially observed panel data. Then, we estimate the factor model using the estimated projected data and construct a covariance matrix estimator. We have established convergence rates of the covariance matrix estimator. Our simulation study shows that although applying projection to partially observed panel data has a trade-off, it generally enhances the covariance matrix estimation accuracy. Its benefit increases with the number of missing entries in a data set.

Keywords: Partially observed panel data, High-dimensional covariance matrix estimation, Characteristic-based factor models, Projected principle component analysis