This paper describes a parameter estimation method for both stationary and non-stationary ARFIMA (p,d,q) models, based on autoregressive approximation. We demonstrate consistency of the estimator for -1/2 < d < 1, and in the stationary case we provide a Normal approximation to the finite-sample distribution which can be used for inference. The method provides good finite-sample performance, comparable with that of ML, and stable performance across a range of stationary and non-stationary values of the fractional differencing parameter. In addition, it appears to be relatively robust to mis-specification of the ARFIMA model to be estimated, and is computationally straightforward.