Minimum distance estimation of ARFIMA processes

This paper proposes a new minimum distance methodology for the estimation of ARFIMA processes with Gaussian and non-Gaussian errors. The main advantage of this method is that it allows for a computationally efficient estimation when the long-memory parameter is in the interval d∈(−12,12). Previous minimum distance estimation techniques are usually limited to the range d∈(−12,14), leaving outside the very important case of strong long memory with d∈[14,12). It is shown that the new estimator satisfies a central limit theorem and Monte Carlo experiments indicate that the proposed estimator performs very well even for small sample sizes. The methodology is illustrated with three applications. The first two examples involve real-life time series while the third application illustrates that the proposed methodology is a sound alternative for dealing with incomplete time series.