  The variability in the magnetic activity of the Sun is the main source of the
observed changes in the plasma and electromagnetic environments within the
heliosphere. The primary way in which solar activity affects the Earth's
environment is via the solar wind and its transients. However, the relationship
between solar activity and solar wind is not the same at the Space Weather and
Space Climate time scales. In this work, we investigate this relationship
exploiting five solar cycles data of Ca II K index and solar wind parameters,
by taking advantage of the Hilbert-Huang Transform, which allows to separate
the contribution at the different time scales. By filtering out the high
frequency components and looking at decennial time scales, we confirm the
presence of a delayed response of solar wind to Ca II K index variations, with
a time lag of ~ 3.1-year for the speed and ~ 3.4-year for the dynamic pressure.
To assess the results in a stronger framework, we make use of a Transfer
Entropy approach to investigate the information flow between the quantities and
to test the causality of the relation. The time lag results from the latter are
consistent with the cross-correlation ones, pointing out the presence of a
statistical significant information flow from Ca II K index to solar wind
dynamic pressure that peaks at time lag of 3.6-year. Such a result could be of
relevance to build up a predictive model in a Space Climate context.
