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Estimation of High-Dimensional Dynamic Conditional Precision Matrices with an Application to Forecast Combination

Author

Listed:
  • Tae-Hwy Lee

    (Department of Economics, University of California Riverside)

  • Millie Yi Mao

    (Azusa Pacific University)

  • Aman Ullah

    (University of California, Riverside)

Abstract

The estimation of a large covariance matrix is challenging when the dimension p is large relative to the sample size n. Common approaches to deal with the challenge have been based on thresholding or shrinkage methods in estimating covariance matrices. However, in many applications (e.g., regression, forecast combination, portfolio selection), what we need is not the covariance matrix but its inverse (the precision matrix). In this paper we introduce a method of estimating the high-dimensional "dynamic conditional precision" (DCP) matrices. The proposed DCP algorithm is based on the estimator of a large unconditional precision matrix by Fan and Lv (2016) to deal with the high-dimension and the dynamic conditional correlation (DCC) model by Engle (2002) to embed a dynamic structure to the conditional precision matrix. The simulation results show that the DCP method performs substantially better than the methods of estimating covariance matrices based on thresholding or shrinkage methods. Finally, inspired by Hsiao and Wan (2014), we examine the "forecast combination puzzle" using the DCP, thresholding, and shrinkage methods.

Suggested Citation

  • Tae-Hwy Lee & Millie Yi Mao & Aman Ullah, 2020. "Estimation of High-Dimensional Dynamic Conditional Precision Matrices with an Application to Forecast Combination," Working Papers 202012, University of California at Riverside, Department of Economics.
    • Handle: RePEc:ucr:wpaper:202012
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    References listed on IDEAS

    as
    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
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    3. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    4. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
    5. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
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    More about this item

    Keywords

    High-dimensional conditional precision matrix; ISEE; DCP; Forecast combination puzzle.;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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