Methods Inf Med 2007; 46(02): 117-120
DOI: 10.1055/s-0038-1625393
Original Article
Schattauer GmbH

Wavelet-based Estimation of Generalized Fractional Process

A. Gonzaga
1   Department of Physical Sciences and Mathematics, University of the Philippines, Manila, Philippines
2   Department of Electrical and Electronics Engineering, Sophia University, Tokyo, Japan
,
A. Kawanaka
2   Department of Electrical and Electronics Engineering, Sophia University, Tokyo, Japan
› Author Affiliations
Further Information

Publication History

Publication Date:
11 January 2018 (online)

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.