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Dynamic partial correlation models

Author

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  • D’Innocenzo, Enzo
  • Lucas, Andre
Abstract
We introduce a new scalable model for dynamic conditional correlation matrices based on a recursion of dynamic bivariate partial correlation models. By exploiting the model’s recursive structure and the theory of perturbed stochastic recurrence equations, we establish stationarity, ergodicity, and filter invertibility in the multivariate setting using conditions for bivariate slices of the data only. From this, we establish consistency and asymptotic normality of the maximum likelihood estimator for the model’s static parameters. The new model outperforms benchmarks like the t-cDCC and the multivariate t-GAS, both in simulations and in an in-sample and out-of-sample asset pricing application to US stock returns.

Suggested Citation

  • D’Innocenzo, Enzo & Lucas, Andre, 2024. "Dynamic partial correlation models," Journal of Econometrics, Elsevier, vol. 241(2).
    • Handle: RePEc:eee:econom:v:241:y:2024:i:2:s0304407624000939
    DOI: 10.1016/j.jeconom.2024.105747
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    References listed on IDEAS

    as
    1. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    2. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
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    6. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
    7. Enzo D’Innocenzo & André Lucas & Bernd Schwaab & Xin Zhang, 2024. "Modeling Extreme Events: Time-Varying Extreme Tail Shape," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 903-917, July.
    8. Hafner, Christian M. & Preminger, Arie, 2009. "Asymptotic Theory For A Factor Garch Model," Econometric Theory, Cambridge University Press, vol. 25(2), pages 336-363, April.
    9. Blasques, Francisco & van Brummelen, Janneke & Koopman, Siem Jan & Lucas, André, 2022. "Maximum likelihood estimation for score-driven models," Journal of Econometrics, Elsevier, vol. 227(2), pages 325-346.
    10. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
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    12. Anne Opschoor & Pawel Janus & André Lucas & Dick Van Dijk, 2018. "New HEAVY Models for Fat-Tailed Realized Covariances and Returns," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 643-657, October.
    13. Anne Opschoor & André Lucas & István Barra & Dick van Dijk, 2021. "Closed-Form Multi-Factor Copula Models With Observation-Driven Dynamic Factor Loadings," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 1066-1079, October.
    14. 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.
    15. Robert F. Engle, 2016. "Dynamic Conditional Beta," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 643-667.
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    22. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
    23. Christian Francq & Jean-Michel Zakoïan, 2016. "Estimating multivariate volatility models equation by equation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 613-635, June.
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    25. Giuseppe Buccheri & Giacomo Bormetti & Fulvio Corsi & Fabrizio Lillo, 2021. "A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: An Application to High-Frequency Covariance Dynamics," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 920-936, October.
    26. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    27. Francisco Blasques & André Lucas & Erkki Silde, 2018. "A stochastic recurrence equations approach for score driven correlation models," Econometric Reviews, Taylor & Francis Journals, vol. 37(2), pages 166-181, February.
    28. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
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