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Sparse Approximate Factor Estimation for High-Dimensional Covariance Matrices


  • Maurizio Daniele

    () (Department of Economics, University of Konstanz, Germany)

  • Winfried Pohlmeier

    (Department of Economics, University of Konstanz, Germany; CoFE; Rimini Centre for Economic Analysis)

  • Aygul Zagidullina

    (Department of Economics, University of Konstanz, Germany)


We propose a novel estimation approach for the covariance matrix based on the l_1-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.

Suggested Citation

  • Maurizio Daniele & Winfried Pohlmeier & Aygul Zagidullina, 2020. "Sparse Approximate Factor Estimation for High-Dimensional Covariance Matrices," Working Paper series 20-03, Rimini Centre for Economic Analysis.
  • Handle: RePEc:rim:rimwps:20-03

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    References listed on IDEAS

    1. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    2. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2011. "A two-step estimator for large approximate dynamic factor models based on Kalman filtering," Journal of Econometrics, Elsevier, vol. 164(1), pages 188-205, September.
    3. repec:hal:journl:peer-00844811 is not listed on IDEAS
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    More about this item


    Approximate Factor model; weak factors; l1-regularization; high dimensional covariance matrix; portfolio allocation;

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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