Multivariate models with long memory dependence in conditional correlation and volatility

Multivariate models with long memory (LM) in conditional correlation and volatility are proposed. The models employ a fractionally integrated version of the dynamic conditional correlation GARCH (DCC-GARCH) process (Engle, 2002), and can be used to forecast conditional covariance matrices of high dimension. The models are applied to a data set consisting of ten US stocks and out of sample forecasts over 1–80 days evaluated using statistical and economic loss functions. If intraday data is unavailable, the statistical loss function reveals that LM correlation models provide superior return covariance matrix forecasts over 20–80 days. When intraday data is available, LM correlation models provide superior forecasts of the realised covariance matrix over the same horizons, however the gains when forecasting the return covariance matrix are small. Finally, when forecasting minimum variance portfolio weights, even though the benefits from LM correlation models diminish completely, they are not consistently outperformed by any of the benchmarks.