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In this paper, we discuss a parsimonious approach to estimation of high-dimensional covariance matrices via the modified Cholesky decomposition with lasso. Two different methods are proposed. They are the equi-angular and equi-sparse methods. We use simulation to compare the performance of the proposed methods with others available in the literature, including the sample covariance matrix, the banding method, and the L₁-penalized normal loglikelihood method. We then apply the proposed methods to a portfolio selection problem using 80 series of daily stock returns. To facilitate the use of lasso in high-dimensional time series analysis, we develop the dynamic weighted lasso (DWL) algorithm that extends the LARS-lasso algorithm. In particular, the proposed algorithm can efficiently update the lasso solution as new data become available. It can also add or remove explanatory variables. The entire …