Abstract In this paper, we studied the long-term memory of Hong Kong Hang Sheng index using MRS analysis, established ARFIMA model for it, and detailed the procedure of fractional differencing. Furthermore, we compared the ARFIMA model built by this means with the one that took first-order differencing as an alternative. The result showed that, if doing so, much useful information of time series would be lost. The forecast formula of ARFIMA model was corrected according to the method of fractional differencing, and was employed in the empirical study. It was illustrated that the forecast performance of ARFIMA model was not as good as we expected since the ARFIMA model was ineffective in forecasting Hang Sheng index. The certainty of this conclusion was proposed from two different aspects.