Wavelet Analysis of Generalized Fractional Process

A generalized fractional process is a fairly general model of long-memory, applicable in modeling many random signals whose autocorrelations exhibit hyperbolic and periodic decay. In this paper, we derive a wavelet-based weighted least squares estimator of the long-memory parameter that is relatively efficient. Results show that the proposed method is relatively computationally and statistically efficient. Moreover it allows for estimation of the long-memory parameter without knowledge of the short-memory parameters, which can be estimated using standard methods. We illustrate our approach by an example applying ECG heart rate data