Specialized topics on financial data analysis from a numerical and physicalpoint of view are discussed. They pertain to the analysis of crash predictionin stock market indices and to the persistence or not of coherent and randomsequences in fluctuations of foreign exchange currency rates. A briefhistorical introduction to crashes is given, including recent observations onthe DJIA and the S&P500. Daily data of the DAX index are specifically used forillustration. The method for visualizing the pattern thought to be theprecursor signature of financial crashes is outlined. The log-periodicity ofthe pattern is investigated. Comparison of patterns before and after crash daysis made through the power spectrum. The corresponding fractal dimension of thesignal looks like that of a percolation backbone. Next the fluctuations ofexchange rates (XR) of currencies forming $EUR$ with respect to $USD$ areanalyzed. The XR power spectra are calculated before and after crashes. Adetrended fluctuation analysis is performed. The characteristic exponents$\beta$ and $\alpha$ respectively, are compared, including the time dependenceof each $\alpha$, found to be singular near crash dates.
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