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Matrix Box-Cox Models for Multivariate Realized Volatility

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  • Roland Weigand

Abstract

We propose exible models for multivariate realized volatility dynamics which involve generalizations of the Box-Cox transform to the matrix case. The matrix Box-Cox model of realized covariances (MBC-RCov) is based on transformations of the covariance matrix eigenvalues, while for the Box-Cox dynamic correlation (BC-DC) specification the variances are transformed individually and modeled jointly with the correlations. We estimate transformation parameters by a new multivariate semiparametric estimator and discuss bias-corrected point and density forecasting by simulation. The methods are applied to stock market data where excellent in-sample and out-of-sample performance is found.

Suggested Citation

  • Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    • Handle: RePEc:bav:wpaper:144_weigand
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    Cited by:

    1. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
    2. Francesco Lautizi, 2015. "Large Scale Covariance Estimates for Portfolio Selection," CEIS Research Paper 353, Tor Vergata University, CEIS, revised 07 Aug 2015.
    3. Ilya Archakov & Peter Reinhard Hansen & Asger Lunde, 2020. "A Multivariate Realized GARCH Model," Papers 2012.02708, arXiv.org.
    4. Ilya Archakov & Peter Reinhard Hansen, 2021. "A New Parametrization of Correlation Matrices," Econometrica, Econometric Society, vol. 89(4), pages 1699-1715, July.
    5. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.

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    More about this item

    Keywords

    realized covariance matrix; dynamic correlation; semiparametric estimation; density forecasting;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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