  In this paper we propose a new early warning test statistic, the ratio of
deviations (RoD), which is defined to be the root mean squared of successive
differences divided by the standard deviation. We show that RoD and
autocorrelation are asymptotically related, and this relationship motivates the
use of RoD to predict Hopf bifurcations in multivariate systems before they
occur. We validate the use of RoD on synthetic data in the novel situation
where the data is sparse and non-uniformly sampled. Additionally, we adapt the
method to be used on high-frequency time series by sampling, and demonstrate
the proficiency of RoD as a classifier.
