Transaction Interval Analysis of High Resolution Foreign Exchange Data

Summary

We analyzed yen-dollar transaction intervals from tick-by-tick data of a 6-month period containing more than a million transactions with time stamps in seconds. We found a fat tail in the distribution of time intervals of successive transactions clearly deviating from the exponential distribution.

In order to clarify the reason for this deviation we introduce the notion of a “locally normalized time interval”, defined by the ratio of a real interval to a moving average of time intervals. We show that the occurrence of market transactions measured by this normalized time is well approximated by a Poisson process.

The best fit for the exponential decay of the interval distribution is when the moving average is taken over the preceding 150 seconds, which indicates that dealers’ perceptions of the market are slowly changing with a time scale of a few minutes. We conclude that the fat tail is due to the slow change of intra-daily transaction rates caused both by the regular activity of business hours and by the market’s spontaneous activity fluctuations.