Abstract 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 on t $t$ 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.

中文翻译：

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带有平滑过渡分数积分参数的广义ARFIMA模型

摘要本文提出了一个时变分数积分模型，其中允许ARFIMA模型中的长存储参数d $ d $依赖于t $ t $并根据先进的平稳过渡回归（STR）模型进行演化由Teräsvirta（1994，1998）撰写。为了估计随时间变化的分数积分参数，我们建议使用瞬时最小二乘估计器（ILSE）基于小波方法的新的多步估计方法。我们进行了一些模拟实验，发现我们的估计迭代过程的性能优于Boutahar，Dufrénot和Péguin-Feissolle（2008）提出的方法。此方法对某些财务时间序列的波动性的经验应用仅用于说明目的。最后，