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Sparse Approximate Factor Estimation for High-Dimensional Covariance Matrices

Maurizio Daniele (), Winfried Pohlmeier and Aygul Zagidullina ()
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Maurizio Daniele: University of Konstanz
Winfried Pohlmeier: University of Konstanz
Aygul Zagidullina: University of Konstanz

No 2018-07, Working Paper Series of the Department of Economics, University of Konstanz from Department of Economics, University of Konstanz

Abstract: We propose a novel estimation approach for the covariance matrix based on the l1-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard approximate factor model. We prove consistency of the covariance matrix estimator under the Frobenius norm as well as the consistency of the factor loadings and the factors. Our Monte Carlo simulations reveal that the SAF covariance estimator has superior properties in finite samples for low and high dimensions and different designs of the covariance matrix. Moreover, in an out-of-sample portfolio forecasting application the estimator uniformly outperforms alternative portfolio strategies based on alternative covariance estimation approaches and modeling strategies including the 1/N-strategy.

Keywords: Approximate Factor model; weak factors; l1-regularization; high dimensional covariance matrix; portfolio allocation (search for similar items in EconPapers)
JEL-codes: C38 C55 G11 G17 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ore
Date: 2018-10-15
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