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A Vector Heterogeneous Autoregressive Index Model for Realized Volatily Measures

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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.

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  • 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
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    2. 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.
    3. Matias Quiroz & Laleh Tafakori & Hans Manner, 2024. "Forecasting realized covariances using HAR-type models," Papers 2412.10791, arXiv.org.
    4. 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.
    5. 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).
    6. 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.
    7. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Feb 2022.
    8. S. Yaser Samadi & Wiranthe B. Herath, 2023. "Reduced-rank Envelope Vector Autoregressive Models," Papers 2309.12902, arXiv.org.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Cubadda, Gianluca & Grassi, Stefano & Guardabascio, Barbara, 2025. "The time-varying Multivariate Autoregressive Index model," International Journal of Forecasting, Elsevier, vol. 41(1), pages 175-190.
    15. Gianluca Cubadda, 2025. "VAR Models with an Index Structure: A Survey with New Results," Econometrics, MDPI, vol. 13(4), pages 1-17, October.
    16. 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.
    17. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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).
    24. Alain Hecq & Ivan Ricardo & Ines Wilms, 2025. "Decomposing Co-Movements in Matrix-Valued Time Series: A Pseudo-Structural Reduced-Rank Approach," Papers 2509.19911, arXiv.org.

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    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

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