An autocovariance-based learning framework for high-dimensional functional time series

Many scientific and economic applications involve the statistical learning of high-dimensional functional time series, where number variables is comparable to, or even greater than, serially dependent observations. In this paper, we model observed which are subject to errors in sense that each datum arises as sum two uncorrelated components, one dynamic white noise. Motivated from fact autocovariance function series automatically filters out noise term, propose a three-step framework by first performing autocovariance-based dimension reduction, then formulating novel block regularized minimum distance estimation produce sparse estimates, based on obtaining final estimates. We investigate theoretical properties proposed estimators, illustrate procedure with corresponding convergence analysis via three models. demonstrate both simulated real datasets our estimators significantly outperform their competitors.