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Multivariate GARCH and portfolio variance prediction: A forecast reconciliation perspective

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  • Massimiliano Caporin
  • Daniele Girolimetto
  • Emanuele Lopetuso

Abstract

We assess the advantage of combining univariate and multivariate portfolio risk forecasts with the aid of forecast reconciliation techniques. In our analyzes, we assume knowledge of portfolio weights, a standard for portfolio risk management applications. With an extensive simulation experiment, we show that, if the true covariance is known, forecast reconciliation improves over a standard multivariate approach, in particular when the adopted multivariate model is misspecified. However, if noisy proxies are used, correctly specified models and the misspecified ones (for instance, neglecting spillovers) turn out to be, in several cases, indistinguishable, with forecast reconciliation still providing improvements. The noise in the covariance proxy plays a crucial role in determining the improvement of both the forecast reconciliation and the correct model specification. An empirical analysis shows how forecast reconciliation can be adopted with real data to improve traditional GARCH-based portfolio variance forecasts.

Suggested Citation

  • Massimiliano Caporin & Daniele Girolimetto & Emanuele Lopetuso, 2026. "Multivariate GARCH and portfolio variance prediction: A forecast reconciliation perspective," Papers 2603.17463, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2603.17463
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    1. Francis X. Diebold & Kamil Yilmaz, 2009. "Measuring Financial Asset Return and Volatility Spillovers, with Application to Global Equity Markets," Economic Journal, Royal Economic Society, vol. 119(534), pages 158-171, January.
    2. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    3. Silva, Felipe L.C. & Souza, Reinaldo C. & Cyrino Oliveira, Fernando L. & Lourenco, Plutarcho M. & Calili, Rodrigo F., 2018. "A bottom-up methodology for long term electricity consumption forecasting of an industrial sector - Application to pulp and paper sector in Brazil," Energy, Elsevier, vol. 144(C), pages 1107-1118.
    4. Carol Alexander, 2002. "Principal Component Models for Generating Large GARCH Covariance Matrices," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 337-359, July.
    5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    6. Patton, Andrew J. & Sheppard, Kevin, 2009. "Optimal combinations of realised volatility estimators," International Journal of Forecasting, Elsevier, vol. 25(2), pages 218-238.
    7. Yuan Gao & Han Lin Shang, 2017. "Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates," Risks, MDPI, vol. 5(2), pages 1-18, March.
    8. Caporale, Guglielmo Maria & Hunter, John & Menla Ali, Faek, 2014. "On the linkages between stock prices and exchange rates: Evidence from the banking crisis of 2007–2010," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 87-103.
    9. Davydenko, Andrey & Fildes, Robert, 2013. "Measuring forecasting accuracy: The case of judgmental adjustments to SKU-level demand forecasts," International Journal of Forecasting, Elsevier, vol. 29(3), pages 510-522.
    10. Li, Han & Li, Hong & Lu, Yang & Panagiotelis, Anastasios, 2019. "A forecast reconciliation approach to cause-of-death mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 122-133.
    11. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    12. 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.
    13. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Panagiotelis, Anastasios, 2024. "Forecast reconciliation: A review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 430-456.
    14. Shanika L. Wickramasuriya & George Athanasopoulos & Rob J. Hyndman, 2019. "Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 804-819, April.
    15. Richard Stone & D. G. Champernowne & J. E. Meade, 1942. "The Precision of National Income Estimates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 9(2), pages 111-125.
    16. Massimiliano Caporin & Michael McAleer, 2008. "Scalar BEKK and indirect DCC," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(6), pages 537-549.
    17. Abolghasemi, Mahdi & Girolimetto, Daniele & Di Fonzo, Tommaso, 2025. "Improving cross-temporal forecasts reconciliation accuracy and utility in energy market," Applied Energy, Elsevier, vol. 394(C).
    18. Laurent, Sébastien & Rombouts, Jeroen V.K. & Violante, Francesco, 2013. "On loss functions and ranking forecasting performances of multivariate volatility models," Journal of Econometrics, Elsevier, vol. 173(1), pages 1-10.
    19. Panagiotelis, Anastasios & Athanasopoulos, George & Gamakumara, Puwasala & Hyndman, Rob J., 2021. "Forecast reconciliation: A geometric view with new insights on bias correction," International Journal of Forecasting, Elsevier, vol. 37(1), pages 343-359.
    20. Shang, Han Lin & Haberman, Steven, 2017. "Grouped multivariate and functional time series forecasting:An application to annuity pricing," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 166-179.
    21. Massimiliano Caporin & Tommaso Di Fonzo & Daniele Girolimetto, 2024. "Exploiting Intraday Decompositions in Realized Volatility Forecasting: A Forecast Reconciliation Approach," Journal of Financial Econometrics, Oxford University Press, vol. 22(5), pages 1759-1784.
    22. Dejan Mircetic & Bahman Rostami-Tabar & Svetlana Nikolicic & Marinko Maslaric, 2022. "Forecasting hierarchical time series in supply chains: an empirical investigation," International Journal of Production Research, Taylor & Francis Journals, vol. 60(8), pages 2514-2533, April.
    23. Hyndman, Rob J. & Ahmed, Roman A. & Athanasopoulos, George & Shang, Han Lin, 2011. "Optimal combination forecasts for hierarchical time series," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2579-2589, September.
    24. Massimiliano Caporin & Paolo Paruolo, 2015. "Proximity-Structured Multivariate Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 559-593, May.
    25. Di Fonzo, Tommaso & Girolimetto, Daniele, 2024. "Forecast combination-based forecast reconciliation: Insights and extensions," International Journal of Forecasting, Elsevier, vol. 40(2), pages 490-514.
    26. Francis X. Diebold & Kamil Yilmaz, 2022. "On the Past, Present, and Future of the Diebold-Yilmaz Approach to Dynamic Network Connectedness," Koç University-TUSIAD Economic Research Forum Working Papers 2207, Koc University-TUSIAD Economic Research Forum.
    27. Annastiina Silvennoinen & Timo Teräsvirta, 2009. "Multivariate GARCH Models," Springer Books, in: Thomas Mikosch & Jens-Peter Kreiß & Richard A. Davis & Torben Gustav Andersen (ed.), Handbook of Financial Time Series, chapter 9, pages 201-229, Springer.
    28. Billio, Monica & Caporin, Massimiliano & Frattarolo, Lorenzo & Pelizzon, Loriana, 2023. "Networks in risk spillovers: A multivariate GARCH perspective," Econometrics and Statistics, Elsevier, vol. 28(C), pages 1-29.
    29. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    30. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    31. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    32. He, Changli & Teräsvirta, Timo, 2004. "An Extended Constant Conditional Correlation Garch Model And Its Fourth-Moment Structure," Econometric Theory, Cambridge University Press, vol. 20(5), pages 904-926, October.
    33. Conrad, Christian & Karanasos, Menelaos, 2010. "Negative Volatility Spillovers In The Unrestricted Eccc-Garch Model," Econometric Theory, Cambridge University Press, vol. 26(3), pages 838-862, June.
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