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Arbitrage chances and the non-Gaussian features of financial data

Although financial time series can be viewed as the random walk for the first approximation, there are many evidences to show deviations from such simple view. First, the empirical probability density distributions of price increments are not Gaussian, but have fat tails. Second, tick-wise motions exhibit certain patterns. Based on those observations we presume that the financial time series carry finite length of memory, which suggest us a possibility of short-term prediction. We have examined large sized tick data of multiple currency exchange rates and found various interesting features such as arbitrage chances observed in triangular trades, the length of memory observed in the tick-wise data, and the scaling property observed in the probability density distribution of price increments.