Intrinsic Mode Cross Correlation: a novel technique to identify scale-dependent lags between two signals and its application to ionospheric science

In this work we address the following question:
can we use modern, cutting edge techniques conceived
for the analysis of nonlinear non-stationary signals to
measure scale-wise lags? To this scope, we propose a
novel technique, called Intrinsic Mode Cross Correlation
method, which leverages on the decomposition of nonlinear
non-stationary signals by the Multivariate Fast Iterative
Filtering (MvFIF) technique and the computation of a scale
by scale cross correlation. We evaluate this technique on
artificial signals (whose ground truth is known) and plasma
density data provided by the Langmuir probes onboard
the Swarm satellites. We show that this technique allows
indeed to reconstruct the lag dependence on the involved
spatio/temporal scales for the artificial data set (even in
presence of high levels of noise), and to estimate them in a
real life signal. This can pave the way to future uses of this
technique in contexts in which the causation chain can be
hidden in a complex, multiscale coupling of the investigated
features.