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Time series occur in many fields of biology, physics, chemistry, engineering. Much workhas been recently performed in statistical physics using specific mathematical techniqueson various time series pertaining to so-called nonlinear phenomena. Severalmethods, beyond the Fourier transform, are presented here. To distinguish betweennoise and deterministic content is the major challenge. Various phenomena are used forillustration. Some emphasis on findings and still questions will be drawn from problemsin finance due to the existence (or not) of long-, medium-, short-range (power-law ornot) correlations in such economic systems. The Fourier transform, the Hurst rescaledrange, the instantaneous detrended fluctuations, the moving averages, and the Zipf-plotsanalysis methods will be recalled. They raise questions about fractional Brownian motionproperties, or in sorting out correlation ranges and predictability. Among spectacularresults, the possibility of crash predictions will be indicated when there is anunderlying discrete scale invariance. Other time series for meteorology and electronicsphenomena are also presented in order to discuss stratus cloud breaking and dielectricbreakdown through avalanches for illustration purpose and to indicate that there areother widely open fields of possible investigations.

Financial Time Series and Statistical Mechanics