On consistency and sparsity for high-dimensional functional time series with application to autoregressions

Guo, Shaojun and Qiao, Xinghao ORCID: 0000-0002-6546-6595 (2023) On consistency and sparsity for high-dimensional functional time series with application to autoregressions. Bernoulli, 29 (1). 451 - 472. ISSN 1350-7265

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Abstract

Modelling a large collection of functional time series arises in a broad spectral of real applications. Under such a scenario, not only the number of functional variables can be diverging with, or even larger than the number of temporally dependent functional observations, but each function itself is an infinite-dimensional object, posing a challenging task. In this paper, we propose a three-step procedure to estimate high-dimensional functional time series models. To provide theoretical guarantees for the three-step procedure, we focus on multivariate stationary processes and propose a novel functional stability measure based on their spectral properties. Such stability measure facilitates the development of some useful concentration bounds on sample (auto)covariance functions, which serve as a fundamental tool for further convergence analysis in high-dimensional settings. As functional principal component analysis (FPCA) is one of the key dimension reduction techniques in the first step, we also investigate the non-asymptotic properties of the relevant estimated terms under a FPCA framework. To illustrate with an important application, we consider vector functional autoregressive models and develop a regularization approach to estimate autoregressive coefficient functions under the sparsity constraint. Using our derived non-asymptotic results, we investigate convergence properties of the regularized estimate under high-dimensional scaling. Finally, the finite-sample performance of the proposed method is examined through both simulations and a public financial dataset.

Item Type:	Article
Official URL:	https://projecteuclid.org/journals/bernoulli
Additional Information:	© 2022 ISI/BS
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	08 Apr 2022 15:42
Last Modified:	12 Dec 2024 02:57
URI:	http://eprints.lse.ac.uk/id/eprint/114638

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