Periodicity detection in irregularly sampled light curves by robust regression and outlier detection

Abstract

An important task in astroparticle physics is the detection of periodicities in irregularly sampled time series, called light curves. Many periodogram methods for light curves may be characterized as fitting periodic models using least squares regression. We generalize this approach and allow robust regression and weighted regression. This gives a unified concept which includes further methods proposed in the literature, allows to create new methods and take additional information about measurement accuracies into account. We compare all these methods using simulated data. We observe that if the quality of the measurement accuracies is dubious, they should be ignored, and that robust methods can be helpful if the light curve contains outliers. Finally, we propose a new way to determine valid periods by robust fitting of a distribution to the periodogram and outlier detection. In our simulations, this leads to better detection rates for periodic fluctuations with unexpected shape and less wrong detections in light curves of pure red and white noise. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 6: 73–89, 2013

RobPer: AnRPackage to Calculate Periodograms for Light Curves Based on Robust Regression

“…The possible shapes of the function g that may be fitted by RobPer are presented in Section 2.1. Fitting them using least squares regression is in many cases equivalent to already existing periodogram methods (see Table 2 or Thieler et al 2013 for a more detailed discussion).…”

“…Another typical periodogram method in astroparticle physics is the phase dispersion minimization periodogram (PDM, Stellingwerf 1978). Depending on the particular setting the periodogram bar in many cases equals the mean of the coefficients of determination of two fits with different step functions with staggered jumps (see Thieler et al 2013or Thieler 2013 for more details).…”

“…M-regression with the Huber function was applied to fit periodic splines by Oh et al (2004). Thieler et al (2013) use least absolute deviations and M-regression and all models described in this article to calculate periodograms based on the coefficient of determination.…”

“…This proceeding incorporates analogues to most of the existing periodograms and introduces several new techniques. Preliminary implementations of most of these periodogram methods have been compared by Thieler, Backes, Fried, and Rhode (2013). Here, we explain the usage of the R package RobPer, which makes improved and extended methods for period detection publicly available.…”

“…Section 3 is devoted to the question how to find valid periods using a periodogram. Thieler et al (2013) propose robust fitting of a beta distribution combined with outlier detection. The function betaCvMfit in the package RobPer performs this.…”