The exact maximum likelihood estimation of ARFIMA processes and model selection criteria: A Monte Carlo study

We propose a detailed Monte Carlo study of model selection criteria when the exact maximum likelihood (EML) method is used to estimate ARFIMA processes. More specifically, our object is to assess the performance of two automatic selection criteria in the presence of long-term memory: Akaike and Schwarz information criteria. Two special processes are considered: a pure fractional noise model (ARFIMA(0,d,0)) and an ARFIMA(1,d,0) process. For each criterion, we compute bias and root mean squared error for various d and AR(1) parameter values. Obtained results suggest that the Schwarz information criterion frequently selects the right model. Moreover, this criterion outperforms the other one in terms of bias and RMSE, for both pure fractional noise and ARFIMA processes.