This paper incorporates conditional heteroscedasticity properties in the long memory model and applies the model on squared returns of BRICS (Brazil, Russia, India, China, and South Africa), UK and USA equity markets to capture the volatility of stock return. The conditional first- and second-order moments are provided. The CLS, FGLS and QML are discussed and 2SQML estimator is proposed. The simulation study suggests that the proposed 2SQML estimator performs better than the other three estimators. Both in simulation and empirical studies, we find that the proposed model FIMACH outperforms FIGARCH in terms of eliminating serial correlations.