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Composite forecasting of vast-dimensional realized covariance matrices using factor state-space models

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  • Jan Patrick Hartkopf

    (University of Cologne)

Abstract

We propose a dynamic factor state-space model for the prediction of high-dimensional realized covariance matrices of asset returns. Using a block LDL decomposition of the joint covariance matrix of assets and factors, we express the realized covariance matrix of the individual assets similar to an approximate factor model. We model the individual parts, i.e., the factor and residual covariances as well as the factor loadings, independently via a tractable state-space approach. This results in closed-form Matrix-F predictive densities for the distinct covariance elements and Student’s t predictive densities for the factor loadings. In an out-of-sample forecasting and portfolio selection exercise we compare the performance of the proposed factor model under different specifications of the residual dynamics. These includes block diagonal residuals based on the GICS sector classifications and strict diagonality assumptions as well as combinations of both using linear shrinkage. We find that the proposed model performs very well in an empirical application to realized covariance matrices for 225 NYSE-traded stocks using the well-known Fama–French factors and sector-specific factors represented by exchange traded funds.

Suggested Citation

  • Jan Patrick Hartkopf, 2023. "Composite forecasting of vast-dimensional realized covariance matrices using factor state-space models," Empirical Economics, Springer, vol. 64(1), pages 393-436, January.
  • Handle: RePEc:spr:empeco:v:64:y:2023:i:1:d:10.1007_s00181-022-02245-1
    DOI: 10.1007/s00181-022-02245-1
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    More about this item

    Keywords

    Factor model; Realized covariance; State-space model; Composite prediction;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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