Comparing the Bias and Misspecification in Arfima Models

A number of papers have looked at the bias in the fractional integration parameter, d using a variety of alternative estimation techniques. This paper supplements that literature by investigating the bias in both the short-term and long-term parameters for a range of ARFIMA models using a more comprehensive range of estimation techniques. The results suggest that all estimation procedures yield slightly biased estimates of the long-run parameter, and that these biases become larger with the introduction of short-term AR or MA parameters. The bias in the short-run parameters mirrors that in the long-run parameters. These biases often causes model selection criteria to select an incorrect ARMA specification, having filtered out the long-run parameter. Incorrect specification of the short-run parameters in the ARFIMA model can accentuate the bias in the long-run parameter.