Measures of periodicity for time series analysis of threshold-crossing events

Large-amplitude climate shifts, the so-called Dansgaard-Oeschger events, repeatedly occurred throughout the last ice age. These events, which are apparently threshold-crossing events, show a reported tendency to recur preferably in near multiples of about 1470 years. Several non-linear resonance mechanisms were proposed to explain this recurrence pattern in response to noise and/or periodic forcing. Standard methods of linear time series analysis are not sufficient to distinguish between these hypotheses, owing to the threshold-crossing dynamics of the events. Recently, new approaches were made by means of null-hypothesis testing with Monte Carlo methods. A major hurdle in this approach is the need of efficient, but yet simple measures of regularity that allow to distinguish between the proposed resonance mechanisms. By means of surrogate time series (i.e. by using a large ensemble of Dansgaard-Oeschger events as simulated with a very simple two-state model) I here test the ability of three standard measures of periodicity to distinguish between a scenario of solely noise-induced events and a ghost stochastic resonance scenario. Only one measure is found to be applicable for that purpose. The choice of adequate measures, which is not trivial, should be given more attention in future studies that focus on the question what triggered threshold-crossing events such as Dansgaard-Oeschger events.