  Specialized topics on financial data analysis from a numerical and physical
point of view are discussed. They pertain to the analysis of crash prediction
in stock market indices and to the persistence or not of coherent and random
sequences in fluctuations of foreign exchange currency rates. A brief
historical introduction to crashes is given, including recent observations on
the DJIA and the S&P500. Daily data of the DAX index are specifically used for
illustration. The method for visualizing the pattern thought to be the
precursor signature of financial crashes is outlined. The log-periodicity of
the pattern is investigated. Comparison of patterns before and after crash days
is made through the power spectrum. The corresponding fractal dimension of the
signal looks like that of a percolation backbone. Next the fluctuations of
exchange rates (XR) of currencies forming $EUR$ with respect to $USD$ are
analyzed. The XR power spectra are calculated before and after crashes. A
detrended fluctuation analysis is performed. The characteristic exponents
$\beta$ and $\alpha$ respectively, are compared, including the time dependence
of each $\alpha$, found to be singular near crash dates.
