A Dynamic Structure for High Dimensional Covariance Matrices and its Application in Portfolio Allocation

Shaojun Guo, John Leigh Box, Wenyang Zhang

Research output: Contribution to journalArticlepeer-review


Estimation of high-dimensional covariance matrices is an interesting and important research topic. In this article, we propose a dynamic structure and develop an estimation procedure for high-dimensional covariance matrices. Asymptotic properties are derived to justify the estimation procedure and simulation studies are conducted to demonstrate its performance when the sample size is finite. By exploring a financial application, an empirical study shows that portfolio allocation based on dynamic high-dimensional covariance matrices can significantly outperform the market from 1995 to 2014. Our proposed method also outperforms portfolio allocation based on the sample covariance matrix, the covariance matrix based on factor models, and the shrinkage estimator of covariance matrix. Supplementary materials for this article are available online.

Original languageEnglish
Pages (from-to)235-253
Number of pages19
JournalJournal of the American Statistical Association
Issue number517
Early online date28 Dec 2015
Publication statusPublished - 2 Jan 2017


  • Dynamic structure
  • Factor models
  • High-dimensional covariance matrices
  • Iterative algorithm
  • Kernel smoothing
  • Portfolio allocation
  • Single-index models

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