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This paper proposes a model of time-varying fractional integration where the long-memory parameter,d   $d$, in an ARFIMA model is allowed to depend ont   $t$and evolve according to a Smooth Transition Regressive (STR) model advanced by  Teräsvirta (1994 ,  1998 ) . To estimate the time-varying fractional integration parameter, we suggest a new multi-step estimation method based on the wavelet approach using the instantaneous least squares estimator (ILSE). We conduct some simulation experiments and we find that our estimation iterative procedure performs better than that proposed by  Boutahar, Dufrénot, and Péguin-Feissolle (2008) . An empirical application of this methodology to the volatility of some financial time series is used for illustration purposes. Finally, it is shown that the model proposed offers an interesting framework to describe long-range dependence in the volatility with heterogeneous persistence.

A Generalized ARFIMA Model with Smooth Transition Fractional Integration Parameter