One of the effects of large dimensionality of data is that even for many low-dimensional functions of the underlying population parameters, such as the mean vector and the covariance matrix, the corresponding sample counterparts are highly biased estimators. In this talk, one such problem is addressed, within the context of determining the mean-variance frontier in financial portfolio optimization. This is done in the time series setting when the vector of returns exhibits temporal dependence. Assuming a specific linear process formulation, an algorithm is proposed to estimate the spectral distributions of the coefficient matrices of the linear process by making use of the asymptotic behavior of the empirical spectral distributions of symmetrized autocovariance matrices. This leads to the formulation of a strategy for the estimation of the mean-variance frontier, utilizing the estimates of the coefficient matrix spectra. (Joint with Haoyang Liu, Florida State; and Debashis Paul, UC Davis.)