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Multivariate Rotated ARCH Models

Author

Listed:
  • Diaa Noureldin

    (Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford)

  • Neil Shephard

    (Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford.)

  • Kevin Sheppard

    (Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford.)

Abstract

This paper introduces a new class of multivariate volatility models which is easy to estimate using covariance targeting, even with rich dynamics. We call them rotated ARCH (RARCH) models. The basic structure is to rotate the returns and then to ?t them using a BEKK-type parameterization of the time-varying covariance whose long-run covariance is the identity matrix. The extension to DCC-type parameterizations is given, introducing the rotated conditional correlation (RCC) model. Inference for these models is computationally attractive, and the asymptotics are standard. The techniques are illustrated using data on some DJIA stocks.

Suggested Citation

  • Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate Rotated ARCH Models," Economics Papers 2012-W01, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:1201
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    Cited by:

    1. Rasmus S. Pedersen & Anders Rahbek, 2014. "Multivariate variance targeting in the BEKK–GARCH model," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 24-55, February.
    2. João F. Caldeira & Guilherme V. Moura & Francisco J. Nogales & André A. P. Santos, 2017. "Combining Multivariate Volatility Forecasts: An Economic-Based Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 15(2), pages 247-285.
    3. Barigozzi, Matteo & Brownlees, Christian & Gallo, Giampiero M. & Veredas, David, 2014. "Disentangling systematic and idiosyncratic dynamics in panels of volatility measures," Journal of Econometrics, Elsevier, vol. 182(2), pages 364-384.
    4. Sensoy, Ahmet & Ozturk, Kevser & Hacihasanoglu, Erk, 2014. "Constructing a financial fragility index for emerging countries," Finance Research Letters, Elsevier, vol. 11(4), pages 410-419.
    5. Bauwens, Luc & Otranto, Edoardo, 2020. "Modelling Realized Covariance Matrices: a Class of Hadamard Exponential Models," LIDAM Discussion Papers CORE 2020034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    7. Yu‐Sheng Lai, 2019. "Flexible covariance dynamics, high‐frequency data, and optimal futures hedging," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(12), pages 1529-1548, December.
    8. Wang, Zihe & Li, Johnny Siu-Hang, 2016. "A DCC-GARCH multi-population mortality model and its applications to pricing catastrophic mortality bonds," Finance Research Letters, Elsevier, vol. 16(C), pages 103-111.
    9. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    10. Manuela Braione & Nicolas K. Scholtes, 2016. "Forecasting Value-at-Risk under Different Distributional Assumptions," Econometrics, MDPI, Open Access Journal, vol. 4(1), pages 1-27, January.
    11. Gian Piero Aielli & Massimiliano Caporin, 2015. "Dynamic Principal Components: a New Class of Multivariate GARCH Models," "Marco Fanno" Working Papers 0193, Dipartimento di Scienze Economiche "Marco Fanno".
    12. repec:gam:jecnmx:v:4:y:2016:i:1:p:3:d:61992 is not listed on IDEAS
    13. Xin Jin & John M. Maheu & Qiao Yang, 2019. "Bayesian parametric and semiparametric factor models for large realized covariance matrices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 641-660, August.
    14. Fiszeder, Piotr & Fałdziński, Marcin, 2019. "Improving forecasts with the co-range dynamic conditional correlation model," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    15. BAUWENS, Luc & BRAIONE, Manuela & STORTI, Giuseppe, 2016. "Multiplicative Conditional Correlation Models for Realized Covariance Matrices," LIDAM Discussion Papers CORE 2016041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. David T. Frazierz & Eric Renault, 2016. "Efficient Two-Step Estimation via Targeting," CIRANO Working Papers 2016s-16, CIRANO.
    17. Manabu Asai & Chia-Lin Chang & Michael McAleer & Laurent Pauwels, 2021. "Asymptotic and Finite Sample Properties for Multivariate Rotated GARCH Models," Econometrics, MDPI, Open Access Journal, vol. 9(2), pages 1-21, May.
    18. Nguyen, Duc Khuong & Sensoy, Ahmet & Sousa, Ricardo M. & Salah Uddin, Gazi, 2020. "U.S. equity and commodity futures markets: Hedging or financialization?," Energy Economics, Elsevier, vol. 86(C).
    19. Brownlees, Christian T., 2019. "Hierarchical GARCH," Journal of Empirical Finance, Elsevier, vol. 51(C), pages 17-27.
    20. Frazier, David T. & Renault, Eric, 2017. "Efficient two-step estimation via targeting," Journal of Econometrics, Elsevier, vol. 201(2), pages 212-227.
    21. Dimitrios P. Louzis, 2015. "The economic value of flexible dynamic correlation models," Economics Bulletin, AccessEcon, vol. 35(1), pages 774-782.
    22. Bauwens, Luc & Grigoryeva, Lyudmila & Ortega, Juan-Pablo, 2016. "Estimation and empirical performance of non-scalar dynamic conditional correlation models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 17-36.
    23. Alfelt, Gustav & Bodnar, Taras & Javed, Farrukh & Tyrcha, Joanna, 2020. "Singular conditional autoregressive Wishart model for realized covariance matrices," Working Papers 2021:1, Örebro University, School of Business.
    24. Wang, Jianshen & Taylor, Nick, 2018. "A comparison of static and dynamic portfolio policies," International Review of Financial Analysis, Elsevier, vol. 55(C), pages 111-127.
    25. Donald Lien & Hsiang‐Tai Lee & Her‐Jiun Sheu, 2018. "Hedging systematic risk in the commodity market with a regime‐switching multivariate rotated generalized autoregressive conditional heteroskedasticity model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(12), pages 1514-1532, December.

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    More about this item

    Keywords

    RARCH; RCC; multivariate volatility; covariance targeting; common persistence; empirical Bayes; predictive likelihood.;
    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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