Regularized estimation of linear functionals for high-dimensional time series

This paper considers regularized estimation of certain linear functionals of high-dimensional linear processes. Our framework covers the broad regime from i.i.d. samples to long-range dependent time series and from sub-Gaussian innovations to those with mild polynomial moments. We show that the regularization parameter and the rate of convergence depend on the degree of temporal dependence and the moment conditions in a subtle way. Ratio consistency is established for the regularized estimator in the context of the sparse Markowitz portfolio allocation and the optimal linear prediction for time series. The effect of dependence and innovation moment conditions is illustrated in the simulation study. Finally, the regularized estimator is applied to classify the cognitive states on a real fMRI dataset and to portfolio optimization on a financial dataset.