Analysis of ultra-high-frequency financial data using advanced Fourier transforms

This paper presents a novel application of advanced methods from Fourier analysis to the study of ultra-high-frequency financial data. The use of Lomb–Scargle Fourier transform, provides a robust framework to take into account the irregular spacing in time, minimising the computational effort. Likewise, it avoids complex model specifications (e.g. ACD or intensity models) or resorting to traditional methods, such as (linear or cubic) interpolation and regular resampling, which not only cause artifacts in the data and loss of information, but also lead to the generation and use of spurious information.