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Temporal aggregation of multivariate GARCH processes

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  • Hafner, Christian M.

Abstract

This paper derives results for the temporal aggregation of multivariate GARCH processes in the general vector specification. It is shown that the class of weak multivariate GARCH processes is closed under temporal aggregation. Fourth moment characteristics turn out to be crucial for the low frequency dynamics for both stock and flow variables. It is shown that spurious instantaneous causality in variance will only appear in degenerated cases, but that spurious Granger causality will be more common. Forecasting volatility, it is generally advisable to aggregate forecasts of the disaggregate series rather than forecasting the aggregated series directly, and unlike for VARMA processes the advantage does not diminish for large forecast horizons. Results are derived for the distribution of multivariate realized volatility if the high frequency process follows multivariate GARCH. Finally, the estimation problem is discussed. A numerical example illustrates some of the results.
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  • Hafner, Christian M., 2008. "Temporal aggregation of multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 142(1), pages 467-483, January.
    • Handle: RePEc:eee:econom:v:142:y:2008:i:1:p:467-483
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    4. Peter Boswijk, H. & van der Weide, Roy, 2011. "Method of moments estimation of GO-GARCH models," Journal of Econometrics, Elsevier, vol. 163(1), pages 118-126, July.
    5. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    6. Erik Kole & Thijs Markwat & Anne Opschoor & Dick van Dijk, 2017. "Forecasting Value-at-Risk under Temporal and Portfolio Aggregation," Journal of Financial Econometrics, Oxford University Press, vol. 15(4), pages 649-677.
    7. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    8. Nicholas Taylor, 2008. "The predictive value of temporally disaggregated volatility: evidence from index futures markets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(8), pages 721-742.
    9. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    10. Morana, Claudio & Sbrana, Giacomo, 2019. "Climate change implications for the catastrophe bonds market: An empirical analysis," Economic Modelling, Elsevier, vol. 81(C), pages 274-294.
    11. Sbrana, Giacomo & Poloni, Federico, 2013. "A closed-form estimator for the multivariate GARCH(1,1) model," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 152-162.
    12. Fengler, Matthias R. & Herwartz, Helmut, 2015. "Measuring spot variance spillovers when (co)variances are time-varying – the case of multivariate GARCH models," Economics Working Paper Series 1517, University of St. Gallen, School of Economics and Political Science.
    13. Babai, M. Zied & Ali, Mohammad M. & Nikolopoulos, Konstantinos, 2012. "Impact of temporal aggregation on stock control performance of intermittent demand estimators: Empirical analysis," Omega, Elsevier, vol. 40(6), pages 713-721.
    14. Leong, Soon Heng & Urga, Giovanni, 2023. "A practical multivariate approach to testing volatility spillover," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    15. Serletis, Apostolos & Xu, Libo, 2016. "Volatility and a century of energy markets dynamics," Energy Economics, Elsevier, vol. 55(C), pages 1-9.
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    18. Yuanyuan Zhang & Rong Liu & Qin Shao & Lijian Yang, 2020. "Two‐Step Estimation for Time Varying Arch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 551-570, July.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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