IDEAS home Printed from
   My bibliography  Save this article

On the Modelling and Forecasting of Multivariate Realized Volatility: Generalized Heterogeneous Autoregressive (GHAR) Model


  • František Čech
  • Jozef Baruník


We introduce a methodology for dynamic modelling and forecasting of realized covariance matrices based on generalization of the heterogeneous autoregressive model (HAR) for realized volatility. Multivariate extensions of popular HAR framework leave substantial information unmodeled in residuals. We propose to employ a system of seemingly unrelated regressions to capture the information. The newly proposed generalized heterogeneous autoregressive (GHAR) model is tested against natural competing models. In order to show the economic and statistical gains of the GHAR model, portfolio of various sizes is used. We find that our modeling strategy outperforms competing approaches in terms of statistical precision, and provides economic gains in terms of mean-variance trade-o. Additionally, our results provide a comprehensive comparison of the performance when realized covariance and more efficient, noise-robust multivariate realized kernel estimator, is used. We study the contribution of both estimators across different sampling frequencies, and we show that the multivariate realized kernel estimator delivers further gains compared to realized covariance estimated on higher frequencies.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • František Čech & Jozef Baruník, 2017. "On the Modelling and Forecasting of Multivariate Realized Volatility: Generalized Heterogeneous Autoregressive (GHAR) Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(2), pages 181-206, March.
  • Handle: RePEc:wly:jforec:v:36:y:2017:i:2:p:181-206

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. 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.
    2. Luo, Jiawen & Chen, Langnan, 2020. "Realized volatility forecast with the Bayesian random compressed multivariate HAR model," International Journal of Forecasting, Elsevier, vol. 36(3), pages 781-799.
    3. Andrea BUCCI, 2017. "Forecasting Realized Volatility A Review," Journal of Advanced Studies in Finance, ASERS Publishing, vol. 8(2), pages 94-138.
    4. Izzeldin, Marwan & Muradoğlu, Yaz Gülnur & Pappas, Vasileios & Sivaprasad, Sheeja, 2021. "The impact of Covid-19 on G7 stock markets volatility: Evidence from a ST-HAR model," International Review of Financial Analysis, Elsevier, vol. 74(C).
    5. Jiawen Luo & Langnan Chen, 2019. "Multivariate realized volatility forecasts of agricultural commodity futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(12), pages 1565-1586, December.
    6. Hwang, Eunju & Hong, Won-Tak, 2021. "A multivariate HAR-RV model with heteroscedastic errors and its WLS estimation," Economics Letters, Elsevier, vol. 203(C).
    7. Lyócsa, Štefan & Molnár, Peter, 2018. "Exploiting dependence: Day-ahead volatility forecasting for crude oil and natural gas exchange-traded funds," Energy, Elsevier, vol. 155(C), pages 462-473.
    8. Zhang, Yongjie & Chu, Gang & Shen, Dehua, 2021. "The role of investor attention in predicting stock prices: The long short-term memory networks perspective," Finance Research Letters, Elsevier, vol. 38(C).
    9. Symitsi, Efthymia & Symeonidis, Lazaros & Kourtis, Apostolos & Markellos, Raphael, 2018. "Covariance forecasting in equity markets," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 153-168.

    More about this item

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jforec:v:36:y:2017:i:2:p:181-206. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.