Evidence for crisis-induced intermittency during geomagnetic superchron transitions.

The geomagnetic field's dipole undergoes polarity reversals in irregular time intervals. Particularly long periods without reversals (of the order of 10^{7} yr), called superchrons, have occurred at least three times in the Phanerozoic (since 541 million years ago). We provide observational evidence for high non-Gaussianity in the vicinity of a transition to and from a geomagnetic superchron, consisting of a sharp increase in high-order moments (skewness and kurtosis) of the dipole's distribution. Such an increase in the moments is a universal feature of crisis-induced intermittency in low-dimensional dynamical systems undergoing global bifurcations. This implies a temporal variation of the underlying parameters of the physical system. Through a low-dimensional system that models the geomagnetic reversals, we show that the increase in the high-order moments during transitions to geomagnetic superchrons is caused by the progressive destruction of global periodic orbits exhibiting both polarities as the system approaches a merging bifurcation. We argue that the non-Gaussianity in this system is caused by the redistribution of the attractor around local cycles as global ones are destroyed.

Kernel Methods for Nonlinear Connectivity Detection.

In this paper, we show that the presence of nonlinear coupling between time series may be detected using kernel feature space F representations while dispensing with the need to go back to solve the pre-image problem to gauge model adequacy. This is done by showing that the kernelized auto/cross sequences in F can be computed from the model rather than from prediction residuals in the original data space X . Furthermore, this allows for reducing the connectivity inference problem to that of fitting a consistent linear model in F that works even in the case of nonlinear interactions in the X -space which ordinary linear models may fail to capture. We further illustrate the fact that the resulting F -space parameter asymptotics provide reliable means of space model diagnostics in this space, and provide straightforward Granger connectivity inference tools even for relatively short time series records as opposed to other kernel based methods available in the literature.

Kernel-nonlinear-PDC extends Partial Directed Coherence to detecting nonlinear causal coupling.

Here we investigate a new concept, kernel-nonlinear-Partial Directed Coherence, whereby a kernel feature space representation of the data allows detecting nonlinear causal links that are otherwise undetectable through linear modeling. We show that adequate connectivity detection is achievable by applying asympotic decision criteria similar to the ones developed for linear models.

Semiparametric detection of nonlinear causal coupling using partial directed coherence.

Infering causal relationships from observed time series has attracted much recent attention. In cases of nonlinear coupling, adequate inference is often hindered by the need to specify coupling details that call for many parameters and global minimization of nonconvex functions. In this paper we use an example to investigate a new concept, termed here running entropy mapping, whereby time series are mapped onto other entropy related time sequences whose analysis via a linear parametric time series methods, such as partial directed coherence, is able to expose the presence of formerly linearly undetectable causal relationships.