Phase dispersion minimization (PDM) is a data analysis technique that searches for periodic components of a time series data set. It is useful for data sets with gaps, non-sinusoidal variations, poor time coverage or other problems that would make Fourier techniques unusable. It was first developed by Stellingwerf in 1978 [1] and has been widely used for astronomical and other types of periodic data analyses. Source code is available for PDM analysis. The current version of this application is available for download.[2]
PDM is a variant of a standard astronomical technique called data folding. This involves guessing a trial period for the data, and cutting, or "folding" the data into multiple sub-series with a time duration equal to the trial period. The data are now plotted versus "phase", or a scale of 0->1, relative to the trial period. If the data is truly periodic with this period a clean functional variation, or "light curve", will emerge. If not the points will be randomly distributed in amplitude.
As early as 1926 Whittiker and Robinson [3] proposed an analysis technique of this type based on maximizing the amplitude of the mean curve. Another technique focusing on the variation of data at adjacent phases was proposed in 1964 by Lafler and Kinman.[4] Both techniques had difficulties, particularly in estimating the significance of a possible solution.
PDM divides the folded data into a series of bins and computes the variance of the amplitude within each bin. The bins can overlap to improve phase coverage, if needed. The bin variances are combined and compared to the overall variance of the data set. For a true period the ratio of the bin to the total variances will be small. For a false period the ratio will be approximately unity. A plot of this ratio versus trial period will usually indicate the best candidates for periodic components. Analyses of the statistical properties of this approach have been given by Nemec & Nemec [5] and Schwarzenberg-Czerny.[6]
The original PDM technique has been updated (PDM2) in several areas::
See reference (2) for a detailed technical discussion, test cases, C source code, and a Windows application package.
In Plavchan et al. 2008,[7] Plavchan introduced a binless version of the phase dispersion minimization algorithm. The algorithm was further revised in 2014 in Parks, Plavchan et al. 2014,[8] and is available for highly-parallel use online at the NASA Exoplanet Archive.[9] The binned PDM approach is susceptible to period aliases when the cadence is semi-regular (e.g., nightly observations of a star brightness). Plavchan and colleagues avoided this aliasing by computing a box-car smoothed phased time-series, where the box-car width can be thought of as the old bin size. The original folded time-series is compared to the smoothed time-series, and the best period is found when the time-series are most similar. See the NASA Exoplanet Archive for more information on statistical significance and approaches.