This paper considers the persistence and asymmetric volatility at each market phase of the Nigerian All Share Index (ASI). The estimate of the fractional difference parameter is used as a stability measure of the degree of persistence in the level of the series and in the absolute/squared returns, which are used as proxies for the volatility. Both semi-parametric and parametric methods are applied. Forms of Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models, which include fractional integration and asymmetric variants are estimated at each market phase of the stock returns. The results show that the level of persistence differs between the two market phases in both level and squared/absolute return series. Apart from general asymmetry and persistence in Nigerian stocks, each market phase still presents significant persistence and asymmetry.