Inverse Statistics in the Foreign Exchange Market

TL;DR

This paper applies inverse statistic analysis to intra-day FX data, revealing resonance peaks linked to trading habits and a new power-law distribution in waiting times, highlighting market activity patterns.

Contribution

It introduces the application of inverse statistics to FX markets and uncovers resonance peaks and a power-law distribution in waiting times, a novel stylized fact.

Findings

Resonance peaks in waiting time distributions linked to trading habits

Power-law distribution observed in rescaled waiting times

Differences between market activity and tick time distributions

Abstract

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) $\rho$ in the price of an investment. The analysis is performed for the Deutsch mark (DM) against the $US for the full year of 1998, but similar results are obtained for the Japanese Yen against the $US. With high statistical significance, the presence of "resonance peaks" in the waiting time distributions is established. Such peaks are a consequence of the trading habits of the markets participants as they are not present in the corresponding tick (business) waiting time distributions. Furthermore, a new {\em stylized fact}, is observed for the waiting time distribution in the form of a power law Pdf. This result is achieved by rescaling of the physical waiting time by the corresponding tick time thereby partially removing scale dependent features of the market activity.