DescriptionThis dissertation studies time-varying high-dimensional covariance matrix estimations. I propose two time-varying covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based factor model, respectively. The models allow factor loadings and error covariance matrices to change over time. I study the rate of convergence of each estimator. My 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 factor loadings, the characteristics can be used to estimate loadings more precisely, making it possible to estimate the covariance matrix more accurately; their helpfulness increases when factor loadings rapidly change or the covariance matrix is larger.