Wavelet Fisher’s Information Measure of 1=f α Signals

Abstract

This article defines the concept of wavelet-based Fisher’s information measure (wavelet FIM) and develops a closed-form expression of this measure for 1=f α signals. Wavelet Fisher’s information measure characterizes the complexities associated to 1=f α signals and provides a powerful tool for their analysis. Theoretical and experimental studies demonstrate that this quantity is exponentially increasing for α > 1 (non-stationary signals) and almost constant for α < 1 (stationary signals). Potential applications of wavelet FIM are discussed in some detail and its power and robustness for the detection of structural breaks in the mean embedded in stationary fractional Gaussian noise signals studied.

Keywords

• 1=f α processes
• structural breaks
• Fisher information
• fractal index estimation
• fractional Gaussian noise