Summary
Objectives
: This paper aims to propose an estimation procedure for the parameters of a generalized
fractional process, a fairly general model of long-memory applicable in modeling biomedical
signals whose autocorrelations exhibit hyperbolic decay.
Methods
: We derive a wavelet-based weighted least squares estimator of the long-memory parameter
based on the maximal-overlap estimator of the wavelet variance. Short-memory parameters
can then be estimated using standard methods. We illustrate our approach by an example
applying ECG heart rate data.
Results and Conclusion
: The proposed method is relatively computationally and statistically efficient. It
allows for estimation of the long-memory parameter without knowledge of the short-memory
parameters. Moreover it provides a more general model of biomedical signals that exhibit
periodic long-range dependence, such as ECG data, whose relatively unobtrusive recording
may be advantageous in assessing or predicting some physiological or pathological
conditions from the estimated values of the parameters.
Keywords
Wavelet coefficients - long-memory - generalized fractional process
