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

Shaojun Guo and Xinghao Qiao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: functional principal component analysis; functional stability measure; high-dimensional functional time series; non-asymptotics; sparsity; vector functional autoregression; Functional principal component analysis (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2023-02-01
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Published in Bernoulli, 1, February, 2023, 29(1), pp. 451 - 472. ISSN: 1350-7265

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:114638

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