Volatility is an inherent characteristic of a time series (TS). It is said to be asymmetric when negative and positive shocks of equal scale have different effects. If the volatility of one epoch is influenced by its distant counterpart, then volatility has a long memory structure. Nonlinear variance models such as the FIEGARCH model are used to deal with asymmetric volatility and long memory simultaneously. This article attempts to derive the direct formulae regarding the ‘out-of-sample’ forecast and the error variances associated with these forecasts for the ARMA(1, 0)- FIEGARCH(1, d, 1) model. Four real-life TS data are used for empirical purposes. It is observed that each TS has a significant long memory in volatility and its volatility is asymmetric.