Spatial-temporal structures in noise processes: microscopic and macroscopic dynamics

Noise processes are often modelled as stochastic processes. We have used a multivariate method based on the application of Principal Component Analysis (PCA) in order to classify different spatial-temporal structures taken as noise. When the structures have a correlation in time, a parameter distinguishing between fast and slow dynamics appears naturally. We have found this parameter in previous contributions with a different meaning depending on the context. Especially interesting is the application to the characterization of 1/f noise. In this paper we have extended the method in order to apply it to different kind of systems exhibiting, for example, self-organizing properties or brownian motion. One goal is trying to define a criterion to distinguish between fast and slow dynamics parameters. Finally, a statistical analysis is made in order to find the conditions for the application of the method to a wide range of different systems.