Autocovariance Function Estimation via Penalized Regression

The work revisits the autocovariance function estimation, a fundamental problem in statistical inference for time series. We convert the function estimation problem into constrained penalized regression with a generalized penalty that provides us with flexible and accurate estimation, and study the asymptotic properties of the proposed estimator. In case of a nonzero mean time series, we apply a penalized regression technique to a differenced time series, which does not require a separate detrending procedure. In penalized regression, selection of tuning parameters is critical and we propose four different data-driven criteria to determine them. A simulation study shows effectiveness of the tuning parameter selection and that the proposed approach is superior to three existing methods. We also briefly discuss the extension of the proposed approach to interval-valued time series. Supplementary materials for this article are available online.