This article compares the performance of bivariate error correction GARCH and FIGARCH models when estimating long term dynamic minimum variance hedge ratios (MVHRs) on the Australian All Ordinaries Index. The paper therefore introduces the bivariate error correction FIGARCH model into the hedging literature, which to date has only employed the GARCH class of processes. This is important for those interested in managing long term equity exposures, given that FIGARCH processes exhibit long memory, whilst the GARCH class of processes exhibit short memory. The naïve hedge ratio, the constant MVHR estimated via ordinary least squares (the OLS MVHR), the single period dynamic MVHR and the multi-period dynamic MVHR of Lee (1999) are considered. The results strongly support the estimation of dynamic MVHRs that allow for time varying correlations. Whilst long memory dependencies appear important, a multi-period dynamic MVHR that responds more rapidly to persistent changes in volatility dynamics requires development.