Let \(X_t\) be, in general, a nonstationary time series. The model under consideration is an autoregressive fractionally integrated moving average (ARFIMA(p,d,q)) model given by \((1-L)^d x_t= (\Theta(L)/\Phi(L)) \epsilon_t\), where \(\epsilon_t\) is a white noise with variance \(\sigma^2\), \(L\) is a lag operator, i.e. \(L^k \epsilon_t = \epsilon_{t-k}\), \(\Theta (L)\) is a moving average polynomial of order \(q\), \(\Phi (L)\) is an autoregressive polynomial of order \(p\) and \(d\) is a real number. This paper examines by means of Monte Carlo simulations the performance of three information criteria such as: (1) AIC criteria, (2) BIC criteria due to Schwarz, (3) Hannan and Quinn criteria HQIC, when order \(d\) must be identified and \(X_t\) is long memory. The author restricted the study to ARFIMA(1,d,1) models and found that BIC outperforms AIC and HQIC, at least for models used in the simulations (only fractional AR or only fractional MA models). BIC behaves consistently, and the underestimation in small samples disappears as the sample size grows. It implies that combining BIC and maximum likelihood gives consistent estimates of the parameters. But it occurs that none of the criteria performs well when there are both AR and MA nonzero parameters in the true process.