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DOI: 10.1055/s-0038-1625393
Wavelet-based Estimation of Generalized Fractional Process
Publication History
Publication Date:
11 January 2018 (online)
![](https://www.thieme-connect.de/media/10.1055-s-00035037/200702/lookinside/thumbnails/10-1055-s-0038-1625393-1.jpg)
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.
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