Time scale defined by the fractal structure of the price fluctuations in foreign exchange markets

Yoshiaki Kumagai
2010 Journal of Physics, Conference Series  
In this contribution, a new time scale named C-fluctuation time is defined by price fluctuations observed at a given resolution. The intraday fractal structures and the relations of the three time scales: real time (physical time), tick time and C-fluctuation time, in foreign exchange markets are analyzed. The data set used is trading prices of foreign exchange rates; US dollar (USD)/Japanese yen (JPY), USD/Euro (EUR), and EUR/JPY. The accuracy of the data is one minute and data within a minute
more » ... ata within a minute are recorded in order of transaction. The series of instantaneous velocity of C-fluctuation time flowing are exponentially distributed for small C when they are measured by real time and for tiny C when they are measured by tick time. When the market is volatile, for larger C, the series of instantaneous velocity are exponentially distributed.
doi:10.1088/1742-6596/221/1/012016 fatcat:553jrdc3m5dp7f2alouo55h4rm