Fractal structure of high-frequency data in the foreign exchange market

In high-frequency financial data, transactions can occur at varying time intervals. We propose a new method to describe the fractal structure of high frequency data, which are non-equidistant in physical time. Using extreme values determined with a scale, we define functions independent of the time scale. Moreover, we can measure a kind of fractal dimension: the fold dimension. Using these functions, we can analyze non-equidistant data without information losses. In this contribution, we use a high frequency data set on bid and ask prices of the dollar/yen exchange rates.