On the gap between an empirical distribution and an exponential distribution of waiting times for price changes in a financial market

Abstract

We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between trades are not exponentially distributed. Here we show that our data is well approximated by a Weibull distribution rather than an exponential distribution in a non-asymptotic regime. Moreover, we quantitatively evaluate how much an empirical data is far from an exponential distribution using a Weibull fit. Finally, we discuss a phase transition between a Weibull-law and a power-law in the asymptotic long waiting time regime.

9 pages, 6 figures, submitted for a publication and under review

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• Waiting-times and returns in high-frequency financial data: an empirical study
• Fractional calculus and continuous-time finance II: the waiting-time distribution
• Waiting times between orders and trades in double-auction markets
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