The effects of high dimensional covariance matrix estimation on asset pricing and generalized least squares.

摘要

Covariance matrix estimation is the essence of measuring risks in multivariate statistics. Existing research efforts are mostly devoted to asymptotic behaviors as sample size increases or to modeling covariance matrices with structural assumptions. In this thesis we investigate alternative methods that do not depend on such restrictions.;High dimensional covariance matrix estimation is considered in the context of empirical asset pricing. In asset pricing models covariance matrices are used more intensively and potentially make significant difference in estimating or testing errors because the nature of asset pricing models is far more complicated. In order to see the effects of covariance matrix estimation on asset pricing, parameter estimation, model specification test, and misspecification problems are explored. Along with existing techniques, which is not yet tested in applications, diagonal variance matrix is simulated to evaluate the performances in these problems. We found that modified Stein type estimator outperforms all the other methods in all three cases. In addition, it turned out that heuristic method of diagonal variance matrix works far better than existing methods in Hansen-Jagannathan distance test.;High dimensional covariance matrix as a transformation matrix in generalized least squares is also studied. Since the feasible generalized least squares estimator requires ex ante knowledge of the covariance structure, it is not applicable in general cases. We propose fully banding strategy for the new estimation technique. Apart from analytical efforts to examine the behaviors of our estimation, guided simulations are provided to support our claim that more spread-out diagonals of covariance matrix lead to better relative outperformance of GLS estimation over OLS estimation. First we look into the sparsity of covariance matrix and the performances of GLS. Then we move onto the discussion of diagonals of covariance matrix and column summation of inverse of covariance matrix to see the effects on GLS estimation. In addition, factor analysis is employed to model the covariance matrix and it turned out that communality truly matters in efficiency of GLS estimation.