Estimation of fractional order of integration in ARFIMA model I wish to model monthly EUR/USD exchange rate by an ARFIMA($p,d,q$) model. 
My question is, how to determine the $d$ parameter of this model? 
 A: Since $d$ can take a continuum of values, there is no simple choice as opposed to the case of integer orders of integration, where you normally choose between $d=0$ and $d=1$ (and, rarely, $d=2$). Software can estimate $d$ for you. In R, check out package "rugarch" and its functions arfimaspec, arfimafit. If you want more details, Ooms & Doornik (1999) consider different ways of estimating ARFIMA models.
References:


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*Ooms, Marius, and Jurgen A. Doornik. Inference and forecasting for fractional autoregressive integrated moving average models, with an application to US and UK inflation. No. EI 9947/A. Econometric Institute, Erasmus University, 1999.

A: Several approaches have been discussed, you must determine if the time series is stationary and if it's a long memory process first. Castaño (2008) suggest to estimate the model $ARFIMA(p^{*},d^{*},0)$ where $p^{*}=round(T^{(1/3)})$ and T the number of observations, if $0< d^{*} \leq 0.5$ then you have to use conventional box-jenkings methods to model the short-memory dependence, that is,to estimate the parameters from: 
$Y_{t} (1-L)^{d^{*}} \quad \sim \quad ARMA(p,q)$ 
for more details go tohttps://revistas.unal.edu.co/index.php/estad/article/view/29594
