String/Rope length methods using the Lafler-Kinman statistic

The original Lafler-Kinman statistic for exploring any auto-correlation within a set of measurements relative to their underlying variance has been regularized so that its determination is independent of the data sample size. In its new form, the power of its application to String-Length period searches (SLLK) has been assessed in terms of establishing confidence levels to point value detections within any generated periodogram and to confidence levels of not missing the detection when an underlying period is present. These estimations depend only on the amplitude of the variation relative to the measurement noise and are independent of the signal-to-noise ratio of the measurements and of their number. Examples of the behaviour of periodograms based on SLLK as produced from computer generated data and real data are discussed. It is also demonstrated that the principle can be readily extended to multivariate data in the form of Rope-Length period searches (RLLK), with the measurements of each parameter not necessarily being taken simultaneously nor with equal number. Using simulated data it is shown that the power of period detection improves slightly if the underlying modulations in each parameter are out of phase with each other. Examples of the RLLK principle are given for computer simulated data and for stellar multi-colour photometric and polarimetric measurements.