Asymmetrical singularities in real-world signals

The singular behavior of real-world signals was investigated by generalizing the wavelet transform modulus maxima (WTMM) approach in order to analyze scaling properties of positive and negative changes separately. The singularity spectra was studied in human heartbeat interval data, time series of daytime human physical activity and daily stock price records of Nikkei. It was demonstrated that a multifractal analysis using wavelets is adequate to the study of nonstationary signals like those encountered in physiological systems. The results concluded that the analysis of asymmetrical singularities provides deep insights into the complexity of real-world signals that can enhance the understanding of the mechanisms determining the systems' dynamics.