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

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JournalJournal of the American Statistical Association
DateAccepted/In press - 2 Dec 2015
DateE-pub ahead of print - 28 Dec 2015
DatePublished (current) - 2017
Issue number517
Volume112
Pages (from-to)235-253
Early online date28/12/15
Original languageEnglish

Abstract

Estimation of high dimensional covariance matrices is an interesting and important research topic. In this paper, 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 factor model given in Fan, Fan and Lv (2008), and the shrinkage estimator given in Ledoit and Wolf (2004).

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