Hi Ahmad, it is the case when the time series has a "long memory", that is (in simple terms) the ACF is decaying slower then normal. As the fractional part is done due to a binomial series, the ARFIMA is to be used for long time series when no additional information which can model the long term dependence (covariates) are available.

http://www.feweb.vu.nl/econometriclinks/ooms/papers/DoornikOoms2004.pdf

Hi Ahmad, it is the case when the time series has a "long memory", that is (in simple terms) the ACF is decaying slower then normal. As the fractional part is done due to a binomial series, the ARFIMA is to be used for long time series when no additional information which can model the long term dependence (covariates) are available.

http://www.feweb.vu.nl/econometriclinks/ooms/papers/DoornikOoms2004.pdf

Thanks Curtef.

Dear Nawaz,

you can detect long memory by the study of residuals of an ARMA model, if the Ljung-Box test gives correlated residuals for a large lag, then it is necessary to model the fractional parameter. See the following paper for computational issues:

http://www.ifop.cl/eyc/files/Contreras_javier/Contreras_Palma-2013.pdf

Good luck, 

Javier E. Contreras-Reyes

https://sites.google.com/site/jcrwebpage

Thank you Javier