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

Abstract

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.

36 pages, 1 figure

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• Methodology and convergence rates for functional linear regression
• Modelling and forecasting daily electricity load curves: a hybrid approach
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• Functional response additive model estimation with online virtual stock markets
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Cited by in corpus (5)

• Factor modelling for high-dimensional functional time series
• Finite Sample Theory for High-Dimensional Functional/Scalar Time Series with Applications
• Factor-guided estimation of large covariance matrix function with conditional functional sparsity
• A Frequency-Domain Approach for Integrating Multiple Functional Time Series
• Factor Models for High-Dimensional Functional Time Series