A different view on data in a nonlinear and nonstationary world

The world we live in is neither stationary nor linear. Yet, the traditional view, based on established mathematical paradigm, is decisively linear and stationary. Such a linear view of the reality has impeded our understanding of the true physical processes. To break away from the inadequacy of the traditional approach, we have to adopt a totally new view with a new data analysis method, for data is the only connection we have with reality. The existing methods such as the probability theory and spectral analysis are all based on global properties of the data, and a priori defined basis and the stationary and linear assumptions. For example, spectral analysis is synonymous with the Fourier-based analysis. As Fourier spectra can only give a meaningful interpretation to linear and stationary processes, its application to data from nonlinear and nonstationary processes is problematical. To break away from this limitation, we should let the data speak for itself. We should develop adaptive data analysis techniques. The basics of the Empirical Mode Decomposition (EMD) and the Hilbert Spectral Analysis (HSA) will be presented. This approach actually offers a different view of the nonlinear and nonstationary world.