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

arXiv: https://arxiv.org/abs/2008.12885 · HTML: https://mlsanity.com/paper/2008.12885/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2020.

## Built on by (most cited first, 1 of 1)

- [Deep Functional Factor Models: Forecasting High-Dimensional Functional Time Series via Bayesian Nonparametric Factorization](https://mlsanity.com/paper/2305.14543/) (2023)

## Abstract (arXiv)

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