Empirical Analysis of Time Series

Time series occur in many fields of biology, physics, chemistry, engineering. Much work has been recently performed in statistical physics using specific mathematical techniques on various time series pertaining to so-called nonlinear phenomena. Several methods, beyond the Fourier transform, are presented here. To distinguish between noise and deterministic content is the major challenge. Various phenomena are used for illustration. Some emphasis on findings and still questions will be drawn from problems in finance due to the existence (or not) of long-, medium-, short-range (power-law or not) correlations in such economic systems. The Fourier transform, the Hurst rescaled range, the instantaneous detrended fluctuations, the moving averages, and the Zipf-plots analysis methods will be recalled. They raise questions about fractional Brownian motion properties, or in sorting out correlation ranges and predictability. Among spectacular results, the possibility of crash predictions will be indicated when there is an underlying discrete scale invariance. Other time series for meteorology and electronics phenomena are also presented in order to discuss stratus cloud breaking and dielectric breakdown through avalanches for illustration purpose and to indicate that there are other widely open fields of possible investigations.