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Causality and forecasting in temporally aggregated multivariate GARCH processes

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  • Christian M. Hafner

Abstract

This paper discusses the effects of temporal aggregation on causality and forecasting in multivariate GARCH processes. It is shown that spurious instantaneous causality in variance will only appear in degenerated cases, but that spurious Granger causality will be more common. For forecasting volatility, it is generally advisable to aggregate forecasts of the disaggregate series rather than forecasting the aggregated series directly, and unlike for vector autoregressive moving average (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. A numerical example illustrates some of the results. Copyright The Author(s). Journal compilation Royal Economic Society 2009

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  • Christian M. Hafner, 2009. "Causality and forecasting in temporally aggregated multivariate GARCH processes," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 127-146, March.
    • Handle: RePEc:ect:emjrnl:v:12:y:2009:i:1:p:127-146
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    Cited by:

    1. Zhang, Hui Jun & Dufour, Jean-Marie & Galbraith, John W., 2016. "Exchange rates and commodity prices: Measuring causality at multiple horizons," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 100-120.
    2. Hafner, Christian M., 2008. "Temporal aggregation of multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 142(1), pages 467-483, January.
    3. Omar Alejandro González Rivas, 2016. "Causalidad en Segundos Momentos: Una aplicación a la volatilidad bursátil en México, Estados Unidos y Australia," Graduate theses (Spanish) TESG 006, CIDE, División de Economía.
    4. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.
    5. Alexander, Carol & Rauch, Johannes, 2021. "A general property for time aggregation," European Journal of Operational Research, Elsevier, vol. 291(2), pages 536-548.

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