Generalized Wavelet Fisher’s Information of\(1/{f}^{\alpha }\)Signals

Abstract

This paper defines the generalized wavelet Fisher information of parameter $q$. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for $1/f^{\alpha }$signals are determined and a detailed discussion of their properties, characteristics and their relationship with wavelet $q$-Fisher information are given. Information planes of $1/f$signals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary $1/f$signals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/ F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of the F-statistic.