This paper is a follow up to Gil-Alana, Shittu and Yaya (2014). In that paper, fractional integration and symmetric volatility modeling were considered on monthly frequency data, while the present paper considers high frequency data on an asymmetric volatility model. The data were first identified within the respective bull and bear phases following earlier results in the previous paper. Then, fractional integration and the asymmetric volatility model of Glosten, Jaganathan and Runkle (GJR) were applied on the stock returns. Long range dependence was detected in the squared stock returns at each market phase, and they were more persistent than those obtained in the monthly frequency data. The estimates of asymmetry of the GJR model actually detected the different patterns of the bad news (bear phases) and the good news (bull phases).