Abstract
This paper utilizes advanced methods from Fourier analysis in order to describe periodicities in financial ultrahigh frequency foreign exchange 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. Furthermore, an event-based approach in intrinsic time based on a power-law relationship is employed using different event thresholds to filter the foreign exchange tick-data. The calculated spectral density demonstrates that the price process in intrinsic time contains different periodic components for directional changes, especially in the medium�long term, implying the existence of stylized facts of ultrahigh frequency data in the frequency domain. Copyright © 2013 John Wiley & Sons, Ltd.
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