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Proximity-Structured Multivariate Volatility Models

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  • Massimiliano Caporin
  • Paolo Paruolo

Abstract

In many multivariate volatility models, the number of parameters increases faster than the cross-section dimension, hence creating a curse of dimensionality problem. This paper discusses specification and identification of structured parameterizations based on weight matrices induced by economic proximity. It is shown that structured specifications can mitigate or even solve the curse of dimensionality problem. Identification and estimation of structured specifications are analyzed, rank and order conditions for identification are given and the specification of weight matrices is discussed. Several structured specifications compare well with alternatives in modelling conditional covariances of six returns from the New York Stock Exchange.

Suggested Citation

  • Massimiliano Caporin & Paolo Paruolo, 2015. "Proximity-Structured Multivariate Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 559-593, May.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:5:p:559-593
    DOI: 10.1080/07474938.2013.807102
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    References listed on IDEAS

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    1. Caporin, Massimiliano & McAleer, Michael, 2014. "Robust ranking of multivariate GARCH models by problem dimension," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 172-185.
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    4. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," CARF F-Series CARF-F-219, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Adam Clements & Mark Doolan & Stan Hurn & Ralf Becker, 2009. "Evaluating multivariate volatility forecasts," NCER Working Paper Series 41, National Centre for Econometric Research, revised 25 Nov 2009.
    6. Caporin Massimiliano & Paruolo Paolo, 2005. "Multivariate ARCH with spatial effects for stock sector and size," Economics and Quantitative Methods qf0509, Department of Economics, University of Insubria.
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    Citations

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    1. Caporin, Massimiliano & Malik, Farooq, 2020. "Do structural breaks in volatility cause spurious volatility transmission?," Journal of Empirical Finance, Elsevier, vol. 55(C), pages 60-82.
    2. 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.
    3. Bonato, Matteo & Caporin, Massimiliano & Ranaldo, Angelo, 2013. "Risk spillovers in international equity portfolios," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 121-137.
    4. Francesco Giuseppe Caloia & Andrea Cipollini & Silvia Muzzioli, 2016. "A note on normalization schemes:The case of generalized forecast error variance decompositions," Department of Economics 0092, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    5. Caloia, Francesco Giuseppe & Cipollini, Andrea & Muzzioli, Silvia, 2019. "How do normalization schemes affect net spillovers? A replication of the Diebold and Yilmaz (2012) study," Energy Economics, Elsevier, vol. 84(C).
    6. Bonaccolto, Giovanni & Caporin, Massimiliano & Panzica, Roberto Calogero, 2017. "Estimation and model-based combination of causality networks," SAFE Working Paper Series 165, Leibniz Institute for Financial Research SAFE.
    7. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar & Wolfgang Schmid & Anil K. Bera, 2023. "Spatial and Spatiotemporal Volatility Models: A Review," Papers 2308.13061, arXiv.org.
    8. Sophie Béreau & Nicolas Debarsy & Cyrille Dossougoin & Jean-Yves Gnabo, 2022. "Contagion in the Banking Industry: a Robust-to-Endogeneity Analysis," Working Papers halshs-03513049, HAL.
    9. Atika Aouri & Philipp Otto, 2025. "A Heterogeneous Spatiotemporal GARCH Model: A Predictive Framework for Volatility in Financial Networks," Papers 2508.20101, arXiv.org.
    10. Valeriya Lakshina, 2014. "Is it possible to break the «curse of dimensionality»? Spatial specifications of multivariate volatility models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 36(4), pages 61-78.
    11. Raffaele Mattera & Philipp Otto, 2023. "Network log-ARCH models for forecasting stock market volatility," Papers 2303.11064, arXiv.org.
    12. Liu, Shaowen & Caporin, Massimiliano & Paterlini, Sandra, 2021. "Dynamic network analysis of North American financial institutions," Finance Research Letters, Elsevier, vol. 42(C).
    13. Francesco Caloia & Andrea Cipollini & Silvia Muzzioli, 2018. "On the financial connectedness of the commodity market: a replication of the Diebold and Yilmaz (2012) study," Department of Economics 0131, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    14. 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.
    15. Bonaccolto, Giovanni & Caporin, Massimiliano & Panzica, Roberto, 2019. "Estimation and model-based combination of causality networks among large US banks and insurance companies," Journal of Empirical Finance, Elsevier, vol. 54(C), pages 1-21.
    16. Carlos Trucíos & Mauricio Zevallos & Luiz K. Hotta & André A. P. Santos, 2019. "Covariance Prediction in Large Portfolio Allocation," Econometrics, MDPI, vol. 7(2), pages 1-24, May.
    17. He, Changli & Kang, Jian & Silvennoinen, Annastiina & Teräsvirta, Timo, 2023. "Long monthly European temperature series and the North Atlantic Oscillation," Energy Economics, Elsevier, vol. 126(C).
    18. 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.
    19. Philipp Otto & Wolfgang Schmid, 2023. "A general framework for spatial GARCH models," Statistical Papers, Springer, vol. 64(5), pages 1721-1747, October.

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