Covariance Function Estimation for High-Dimensional Functional Time Series with Dual Factor Structures

Chenlei Leng, Degui Li, Hanlin Shang and Yingcun Xia
Additional contact information
Chenlei Leng: University of Warwick
Hanlin Shang: Macquarie University
Yingcun Xia: National University of Singapore

No 202524, Working Papers from University of Macau, Faculty of Business Administration

Abstract: We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor structure is imposed on the observed functional processes, whereas a low-dimensional version (via series approximation) is assumed for the latent functional factors. We extend the classic principal component analysis technique for estimating a low-rank structure to the estimation of a large covariance matrix of random functions that satisfies a notion of (approximate) functional “low-rank plus sparse” structure; and generalize the matrix shrinkage method to functional shrinkage in order to estimate the sparse structure of functional idiosyncratic components. The developed methodology can be used to estimate both the functional contemporaneous covariance and lag-hautocovariance matrices. Under appropriate regularity conditions, we derive the large sample theory of the resulting estimators, including the consistency of the estimated factors and functional factor loadings and the convergence rates of the estimated matrices of covariance and autocovariance functions measured by various (functional) matrix norms. Consistent selection of the number of factors and a data-driven rule to choose the shrinkage parameter are discussed. Simulation and empirical studies are provided to demonstrate the finite-sample performance of the developed model and estimation methodology.

Keywords: Covariance operator; functional factor model; functional time series; generalized shrink-age; high dimensionality; PCA; sparsity (search for similar items in EconPapers)
JEL-codes: C13 C55 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2025-03
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Published in UM-FBA Working Paper Series

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Working Paper: Covariance Function Estimation for High-Dimensional Functional Time Series with Dual Factor Structures (2024)
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