Detection of periodicity based on independence tests – III. Phase distance correlation periodogram

Abstract

I present the Phase Distance Correlation (PDC) periodogram -a new periodicity metric, based on the Distance Correlation concept of Gábor Székely. For each trial period PDC calculates the distance correlation between the data samples and their phases. PDC requires adaptation of the Székely's distance correlation to circular variables (phases). The resulting periodicity metric is best suited to sparse datasets, and it performs better than other methods for sawtooth-like periodicities. These include Cepheid and RR-Lyrae light curves, as well as radial velocity curves of eccentric spectroscopic binaries. The performance of the PDC periodogram in other contexts is almost as good as that of the Generalized Lomb-Scargle periodogram. The concept of phase distance correlation can be adapted also to astrometric data, and it has the potential to be suitable also for large evenly-spaced datasets, after some algorithmic perfection.

A Transiting Warm Giant Planet around the Young Active Star TOI-201

“…In order to further verify that the ∼53 day signal is planetary in nature, we also computed the Phase Distance Correlation (PDC) periodogram (Zucker 2018) for the FEROS data. We find a stronger signal at the 53 day period in the PDC periodogram than in a comparison GLS periodogram, as expected for eccentric orbits, as shown in Figure 6.…”

USuRPER: Unit-sphere representation periodogram for full spectra

“…In other words, it is actually the normalised correlation between the two original spectra, henceforth C i j . Now that we have defined a distance function, it might appear that we can calculate the two required distance matrices, following Zucker (2018Zucker ( , 2019. However, the space on which our distance function (Eq.…”

“…cyclic), we have modified the original expression of Székely et al (2007), following their original derivation, but for circular variables. As we have shown (Zucker 2018), the newly introduced periodogram outperforms other methods in cases of sawtooth-like variability shapes, including also radial velocity (RV) curves of eccentric single-lined spectroscopic binary (SB1) stars.…”

“…In two previous papers (Zucker 2018(Zucker , 2019, we have introduced the phase-distance correlation (PDC) periodogram as a new method to detect non-sinusoidal periodicities in unevenly sampled time-series data. Essentially, for each trial period, PDC quantifies the statistical dependence between the measured quantity and the phase (according to the trial period), using the recently introduced distance correlation.…”

Detection of periodicity based on independence tests – IV. Phase distance correlation periodogram for two-dimensional astrometry

“…In the three previous papers in this series (Zucker 2015(Zucker , 2016(Zucker , 2018 hereafter Paper I, Paper II and Paper III), I have introduced a new non-parametric approach to the detection of periodicities in sparse data sets. The first two papers followed the logic of string-length techniques (e.g., Lafler & Kinman 1965;Clarke 2002) and presented a way to quantify the dependence between consecutive phase-folded samples (serial dependence), for every trial period.…”