Estimation of The Long-Range Dependence Parameter of Fractional Arima Processes

The most well-known models of long-range dependent processes are fractional Gaussian noise [7] (thus secondorder self-similarity) and fractional ARIMA [3, 4]. Each of these models has a corresponding long-range dependence parameter. Since the value of the parameter indicates the intensity of this dependence structure, it is important to have a better tool to estimate it. Such an estimator should not be biased and the confidence intervals should be as small as possible. Moreover, if we would like to estimate the parameter on-line, then the estimation tool should be as fast as possible. Several methods for estimating long-range dependence parameters have been proposed; see [2] for details. By far, the wavelet method is the most widely used. When a process is assumed to be second-order self-similar, [6] introduced a new method that uses the structure of the covariance function to estimate the Hurst parameter. The method was shown to be much faster and yield smaller confidence intervals than the wavelet method. In this paper, we consider the case when the process is assumed to be fractional ARIMA and show that the new method still possesses the aforementioned qualities.