Causality and forecasting in temporally aggregated multivariate GARCH processes

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.