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A smooth transition long-memory model

Marcel Aloy EMAIL logo , Gilles Dufrénot , Charles Lai Tong and Anne Peguin-Feissolle


This paper proposes a new fractional model with a time-varying long-memory parameter. The latter evolves nonlinearly according to a transition variable through a logistic function. We present an LR-Based test that allows to discriminate between the standard fractional model and our model. We further apply a nonlinear least squares estimation method to estimate the long-memory parameter. We present an application to the unemployment rate in the United States from 1948 to 2012.

Corresponding author: Marcel Aloy, Aix-Marseille University (Aix-Marseille School of Economics), CNRS & EHESS, GREQAM, Centre de la Charité, 2 rue de la Charité, 13236 Marseille Cedex 02, France

  1. 1

    The case d(1)>0.5 and d(S)>0.5 is examined, in addition to the stationarity case, in order to see how the test behaves in the non-stationary case. From Table 3 we see that the rejection frequencies compare well with the stationary case.


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Published Online: 2013-04-08
Published in Print: 2013-05-01

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