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

High dimensional covariance matrix estimation is considered in the context of empirical asset pricing. 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. 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.