Estimation of Large Dynamic Covariance Matrices: A Selective Review

Degui Li

doi:10.1016/j.ecosta.2021.04.008

Estimation of Large Dynamic Covariance Matrices: A Selective Review

Degui Li

Mathematics

Research output: Contribution to journal › Review article › peer-review

Abstract

A personal review of some recent developments on estimating large dynamic covariance matrices whose entries are allowed to change over time is provided. The underlying covariance matrices are assumed to satisfy structural assumptions such as GARCH, approximate sparsity and conditional sparsity. Initially the review considers extensions of the classic GARCH model to multivariate and high-dimensional time series settings, and then focuses on some data-driven non- and semi-parametric models and estimation approaches for large covariance matrices which evolve smoothly over time or with some conditioning variables. Detection of multiple structural breaks in large covariance structures is also reviewed. Finally some relevant future directions are discussed.

Original language	English
Pages (from-to)	16-30
Number of pages	15
Journal	Econometrics and Statistics
Volume	29
Early online date	21 Dec 2023
DOIs	https://doi.org/10.1016/j.ecosta.2021.04.008
Publication status	Published - 1 Jan 2024

Bibliographical note

Access to Document

10.1016/j.ecosta.2021.04.008

Embargoed Document

Li-ECOSTA-D-20-00256R1
Accepted author manuscript, 311 KB
Licence: CC BY-NC-ND
Embargo ends: 21/06/25

Cite this

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abstract = "A personal review of some recent developments on estimating large dynamic covariance matrices whose entries are allowed to change over time is provided. The underlying covariance matrices are assumed to satisfy structural assumptions such as GARCH, approximate sparsity and conditional sparsity. Initially the review considers extensions of the classic GARCH model to multivariate and high-dimensional time series settings, and then focuses on some data-driven non- and semi-parametric models and estimation approaches for large covariance matrices which evolve smoothly over time or with some conditioning variables. Detection of multiple structural breaks in large covariance structures is also reviewed. Finally some relevant future directions are discussed.",

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