Comparing the bias and misspecification in ARFIMA models

Abstract

We investigate the bias in both the short‐term and long‐term parameters for a range of autoregressive fractional integrated moving‐average (ARFIMA) models using both semi‐parametric and maximum likelihood (ML) estimation methods. The results suggest that, provided the correct model is estimated, the ML method outperforms the semi‐parametric methods in terms of the bias and smaller mean square errors in both the long‐term and short‐term parameter estimates. These biases often cause model selection criteria to select an incorrect ARFIMA specification. Taking account of the potential misspecification the biases associated with the ML procedure tend to increase, although it continues to have a smaller worst‐case bias than either of the semi‐parametric procedures.