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Sparse Approximate Factor Estimation for High-Dimensional Covariance Matrices

Author

Listed:
  • 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)

Abstract

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

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    Cited by:

    1. Dashan Huang & Fuwei Jiang & Kunpeng Li & Guoshi Tong & Guofu Zhou, 2022. "Scaled PCA: A New Approach to Dimension Reduction," Management Science, INFORMS, vol. 68(3), pages 1678-1695, March.
    2. Giorgio Calzolari & Roxana Halbleib & Christian Mucher, 2023. "Sequential Estimation of Multivariate Factor Stochastic Volatility Models," Papers 2302.07052, arXiv.org.
    3. Maurizio Daniele & Julie Schnaitmann, 2019. "A Regularized Factor-augmented Vector Autoregressive Model," Papers 1912.06049, arXiv.org.

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    More about this item

    Keywords

    Approximate Factor model; weak factors; l1-regularization; high dimensional covariance matrix; portfolio allocation;
    All these keywords.

    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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