Wavelet-based Estimation of Generalized Fractional Process - Gonzaga, A.; Kawanaka, A. (Methods of Information in Medicine, 2007)
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