IDEAS home Printed from https://ideas.repec.org/p/rtv/ceisrp/391.html
   My bibliography  Save this paper

A Vector Heterogeneous Autoregressive Index Model for Realized Volatily Measures

Author

Listed:

Abstract

This paper introduces a new modelling for detecting the presence of commonalities in a set of realized volatility measures. In particular, we propose a multivariate generalization of the heterogeneous autoregressive model (HAR) that is endowed with a common index structure. The Vector Heterogeneous Autoregressive Index model has the property to generate a common index that preserves the same temporal cascade structure as in the HAR model, a feature that is not shared by other aggregation methods (e.g., principal components). The parameters of this model can be easily estimated by a proper switching algorithm that increases the Gaussian likelihood at each step. We illustrate our approach with an empirical analysis aiming at combining several realized volatility measures of the same equity index for three di?erent markets.

Suggested Citation

  • Gianluca Cubadda & Barbara Guardabascio & Alain Hecq, 2016. "A Vector Heterogeneous Autoregressive Index Model for Realized Volatily Measures," CEIS Research Paper 391, Tor Vergata University, CEIS, revised 23 Jul 2016.
    • Handle: RePEc:rtv:ceisrp:391
    as

    Download full text from publisher

    File URL: https://ceistorvergata.it/RePEc/rpaper/RP391.pdf
    File Function: Main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fengler, Matthias R. & Gisler, Katja I.M., 2015. "A variance spillover analysis without covariances: What do we miss?," Journal of International Money and Finance, Elsevier, vol. 51(C), pages 174-195.
    2. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
    3. Hecq Alain & Laurent Sébastien & Palm Franz C., 2016. "On the Univariate Representation of BEKK Models with Common Factors," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 91-113, July.
    4. Bubák, Vít & Kocenda, Evzen & Zikes, Filip, 2011. "Volatility transmission in emerging European foreign exchange markets," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2829-2841, November.
    5. Patton, Andrew J., 2011. "Data-based ranking of realised volatility estimators," Journal of Econometrics, Elsevier, vol. 161(2), pages 284-303, April.
    6. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    7. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    8. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    9. Bernardini, Emmanuela & Cubadda, Gianluca, 2015. "Macroeconomic forecasting and structural analysis through regularized reduced-rank regression," International Journal of Forecasting, Elsevier, vol. 31(3), pages 682-691.
    10. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    11. Anderson, Heather M. & Vahid, Farshid, 2007. "Forecasting the Volatility of Australian Stock Returns: Do Common Factors Help?," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 76-90, January.
    12. Engle, Robert F & Susmel, Raul, 1993. "Common Volatility in International Equity Markets," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 167-176, April.
    13. Souček, Michael & Todorova, Neda, 2013. "Realized volatility transmission between crude oil and equity futures markets: A multivariate HAR approach," Energy Economics, Elsevier, vol. 40(C), pages 586-597.
    14. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    15. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    16. Gianluca Cubadda & Alain Hecq, 2011. "Testing for common autocorrelation in data‐rich environments," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(3), pages 325-335, April.
    17. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2009. "Studying co-movements in large multivariate data prior to multivariate modelling," Journal of Econometrics, Elsevier, vol. 148(1), pages 25-35, January.
    18. Engle, Robert F. & Marcucci, Juri, 2006. "A long-run Pure Variance Common Features model for the common volatilities of the Dow Jones," Journal of Econometrics, Elsevier, vol. 132(1), pages 7-42, May.
    19. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. H. Peter Boswijk & Jurgen A. Doornik, 2004. "Identifying, estimating and testing restricted cointegrated systems: An overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 440-465, November.
    21. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    22. Patton, Andrew J. & Sheppard, Kevin, 2009. "Optimal combinations of realised volatility estimators," International Journal of Forecasting, Elsevier, vol. 25(2), pages 218-238.
    23. Yanagihara, Hirokazu, 2006. "Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1070-1089, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Gianluca Cubadda & Alain Hecq, 2021. "Reduced Rank Regression Models in Economics and Finance," CEIS Research Paper 525, Tor Vergata University, CEIS, revised 08 Nov 2021.
    2. Wang, Jiqian & Lu, Xinjie & He, Feng & Ma, Feng, 2020. "Which popular predictor is more useful to forecast international stock markets during the coronavirus pandemic: VIX vs EPU?," International Review of Financial Analysis, Elsevier, vol. 72(C).
    3. S. Yaser Samadi & Wiranthe B. Herath, 2023. "Reduced-rank Envelope Vector Autoregressive Models," Papers 2309.12902, arXiv.org.
    4. 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.
    5. Caloia, Francesco Giuseppe & Cipollini, Andrea & Muzzioli, Silvia, 2018. "Asymmetric semi-volatility spillover effects in EMU stock markets," International Review of Financial Analysis, Elsevier, vol. 57(C), pages 221-230.
    6. Wilms, Ines & Rombouts, Jeroen & Croux, Christophe, 2021. "Multivariate volatility forecasts for stock market indices," International Journal of Forecasting, Elsevier, vol. 37(2), pages 484-499.
    7. Gianluca Cubadda & Marco Mazzali, 2024. "The vector error correction index model: representation, estimation and identification," The Econometrics Journal, Royal Economic Society, vol. 27(1), pages 126-150.
    8. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
    9. Jian, Zhihong & Deng, Pingjun & Zhu, Zhican, 2018. "High-dimensional covariance forecasting based on principal component analysis of high-frequency data," Economic Modelling, Elsevier, vol. 75(C), pages 422-431.
    10. Bauwens, Luc & Braione, Manuela & Storti, Giuseppe, 2017. "A dynamic component model for forecasting high-dimensional realized covariance matrices," Econometrics and Statistics, Elsevier, vol. 1(C), pages 40-61.
    11. G. Cubadda & S. Grassi & B. Guardabascio, 2022. "The Time-Varying Multivariate Autoregressive Index Model," Papers 2201.07069, arXiv.org.
    12. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    13. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Feb 2022.
    14. Gianluca Cubadda & Alain Hecq & Antonio Riccardo, 2018. "Forecasting Realized Volatility Measures with Multivariate and Univariate Models: The Case of The US Banking Sector," CEIS Research Paper 445, Tor Vergata University, CEIS, revised 30 Oct 2018.
    15. Cubadda, Gianluca & Guardabascio, Barbara, 2019. "Representation, estimation and forecasting of the multivariate index-augmented autoregressive model," International Journal of Forecasting, Elsevier, vol. 35(1), pages 67-79.
    16. Yaojie Zhang & Yudong Wang & Feng Ma, 2021. "Forecasting US stock market volatility: How to use international volatility information," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(5), pages 733-768, August.
    17. Won-Tak Hong & Jiwon Lee & Eunju Hwang, 2020. "A Note on the Asymptotic Normality Theory of the Least Squares Estimates in Multivariate HAR-RV Models," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    18. Ma, Feng & Wahab, M.I.M. & Zhang, Yaojie, 2019. "Forecasting the U.S. stock volatility: An aligned jump index from G7 stock markets," Pacific-Basin Finance Journal, Elsevier, vol. 54(C), pages 132-146.
    19. Chao Liang & Yu Wei & Yaojie Zhang, 2020. "Is implied volatility more informative for forecasting realized volatility: An international perspective," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(8), pages 1253-1276, December.
    20. Qiao, Gaoxiu & Yang, Jiyu & Li, Weiping, 2020. "VIX forecasting based on GARCH-type model with observable dynamic jumps: A new perspective," The North American Journal of Economics and Finance, Elsevier, vol. 53(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gianluca Cubadda & Alain Hecq & Antonio Riccardo, 2018. "Forecasting Realized Volatility Measures with Multivariate and Univariate Models: The Case of The US Banking Sector," CEIS Research Paper 445, Tor Vergata University, CEIS, revised 30 Oct 2018.
    2. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    3. Gianluca Cubadda & Alain Hecq, 2021. "Reduced Rank Regression Models in Economics and Finance," CEIS Research Paper 525, Tor Vergata University, CEIS, revised 08 Nov 2021.
    4. Bu, Ruijun & Hizmeri, Rodrigo & Izzeldin, Marwan & Murphy, Anthony & Tsionas, Mike, 2023. "The contribution of jump signs and activity to forecasting stock price volatility," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 144-164.
    5. Yaojie Zhang & Yudong Wang & Feng Ma & Yu Wei, 2022. "To jump or not to jump: momentum of jumps in crude oil price volatility prediction," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-31, December.
    6. Bekierman, Jeremias & Manner, Hans, 2018. "Forecasting realized variance measures using time-varying coefficient models," International Journal of Forecasting, Elsevier, vol. 34(2), pages 276-287.
    7. Lyócsa, Štefan & Molnár, Peter & Todorova, Neda, 2017. "Volatility forecasting of non-ferrous metal futures: Covariances, covariates or combinations?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 51(C), pages 228-247.
    8. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    9. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.
    10. Chorro, Christophe & Ielpo, Florian & Sévi, Benoît, 2020. "The contribution of intraday jumps to forecasting the density of returns," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    11. D. Schneller & S. Heiden & M. Heiden & A. Hamid, 2018. "Home is Where You Know Your Volatility – Local Investor Sentiment and Stock Market Volatility," German Economic Review, Verein für Socialpolitik, vol. 19(2), pages 209-236, May.
    12. Douglas G. Santos & Flavio A. Ziegelmann, 2014. "Volatility Forecasting via MIDAS, HAR and their Combination: An Empirical Comparative Study for IBOVESPA," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(4), pages 284-299, July.
    13. Chao Zhang & Xingyue Pu & Mihai Cucuringu & Xiaowen Dong, 2023. "Graph Neural Networks for Forecasting Multivariate Realized Volatility with Spillover Effects," Papers 2308.01419, arXiv.org.
    14. Todorova, Neda, 2015. "The course of realized volatility in the LME non-ferrous metal market," Economic Modelling, Elsevier, vol. 51(C), pages 1-12.
    15. Gallo, Giampiero M. & Otranto, Edoardo, 2015. "Forecasting realized volatility with changing average levels," International Journal of Forecasting, Elsevier, vol. 31(3), pages 620-634.
    16. Stefan Lyocsa & Peter Molnar & Igor Fedorko, 2016. "Forecasting Exchange Rate Volatility: The Case of the Czech Republic, Hungary and Poland," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 66(5), pages 453-475, October.
    17. Yang, Ke & Tian, Fengping & Chen, Langnan & Li, Steven, 2017. "Realized volatility forecast of agricultural futures using the HAR models with bagging and combination approaches," International Review of Economics & Finance, Elsevier, vol. 49(C), pages 276-291.
    18. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Post-Print halshs-01442618, HAL.
    19. Gkillas, Konstantinos & Gupta, Rangan & Pierdzioch, Christian, 2020. "Forecasting realized oil-price volatility: The role of financial stress and asymmetric loss," Journal of International Money and Finance, Elsevier, vol. 104(C).
    20. Wilms, Ines & Rombouts, Jeroen & Croux, Christophe, 2021. "Multivariate volatility forecasts for stock market indices," International Journal of Forecasting, Elsevier, vol. 37(2), pages 484-499.

    More about this item

    Keywords

    Common volatility; HAR models; index models; combinations of realized volatil¬ities; forecasting;
    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    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:rtv:ceisrp:391. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Barbara Piazzi (email available below). General contact details of provider: https://edirc.repec.org/data/csrotit.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.