On the base is of ARFIMA model and smooth transition model which describe long memory and structural change respectively, this paper proposes a STARFIMA model to jointly test these two proper- ties of time series and presents the methods of parameter estimation and bootstrap likelihood ratio test for null of linearity. As a case of China's inflation rate, we find that STARFIMA model can simulate better than the linear ARFIMA model by empirical analysis with logistic smooth transition ARFIMA model. Moreover, this model can capture structural change with transition variables of inflation rate and increasing inflation rate, and the results suggest that the memory becomes strong when considering structural change and displays long range dependence.

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