For quite a long time, numerical analysis of time series derived from the stock, foreign exchange markets have been attempted. In this book, nonlinear data analysis tools are used to explore the rich dynamics of the financial time series. During analyses, it was found that what seems to be chaotic, unpredictable in smaller scale of days or weeks, may appear as increasing/decreasing in longer scale, mimicking some polynomial fit. Another particularly interesting feature of these data are their self-similar nature. That again brings forth a scope of fractal based analysis.During the analyses of financial time series data, we worked with raw data- that is as they are available from the respective markets. We did not take into account the noise (that is the unwanted signal) that are present in data sets under analysis. During our visit at Istanbul Technical University, Turkey, 2009 we had very fruitful discussion with C. Gursan and Prof. Ali H. Buyuklu on this topic which finalized as the last chapter of this book where we attempt to work out algorithm to check Signal to Noise Ratio (SNR).