Periodicities of FX Markets in Intrinsic Time

This paper utilises advanced methods from Fourier Analysis in order to describe financial ultra-high frequent transaction data. The Lomb-Scargle Fourier Transform is used to take into account the irregularity in spacing in the time-domain. It provides a natural framework for the power spectra of different inhomogeneous time series processes to be easily and quickly estimated,without significant computational effort, in contrast to the common econometric approaches in the finance literature. An event-based approach (intrinsic time), which by its own nature is inhomogeneous in time, is employed using different event thresholds to filter the foreign exchange tick-data leading to a power-law relationship. The calculated spectral density demonstrates that the price process in intrinsic time contains different periodic components, especially in the medium-long term, implying the existence of new stylised facts of ultra-high frequency data in the frequency domain.