The Identi cation ofFractional ARIMA

For the fractional ARIMA model, we demonstrate that wrong model speciication might lead to serious problems of inference in nite samples. We assess the performance of various model selection criteria when the true model is fractionally integrated and the alternatives of interest are ARMA and fractional ARIMA models. The likelihood of successful identiication increases substantially with rising sample size and varies across selection criteria. The Schwarz Criterion performs best in the detection of fractionally diierenced noise. For general fractional ARIMA models the choice of criterion is a tradeoo between the detection of dominated weak stochastic components and possible overparameterization. Sloan Foundation for its Doctoral Dissertation Fellowship, and of the Deutsche Forschungsge-meinschaft (DFG). Part of this work is based on the doctoral dissertation of the second author at the University of Munich. A preliminary version of this paper had the title "Identiication of Fractional ARIMA Models in the Presence of Long Memory". The research was continued within the Sonderforschungsbereich 373 at the Humboldt University Berlin which is funded by the Deutsche Forschungsgemeinschaft. The authors are grateful for comments to JJ org Breitung,