Wavelet Analysis of Generalized Fractional Process

• Published in: 2005 5th International Conference on Information Communications and Signal Processing pp. 69 - 72
• Main Authors: Gonzaga, A., Kawanaka, A.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2005
• Subjects: Autocorrelation; Autoregressive processes; Frequency; Generalized fractional process; Heart rate; Least squares approximation; Long-memory; Mathematical model; Maximum likelihood estimation; Pediatrics; Wavelet analysis; Wavelet coefficients; White noise
• ISBN: 9780780392830; 0780392833
• DOI: 10.1109/ICICS.2005.1689006

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