  The solar activity, which is driven by a variable magnetic field, exhibits
changes along several time scales, the 11-year being the most known. In
addition to the SunSpot Number, the Ca II K index and the Mg II index are
indices widely employed among those proposed to quantify the solar activity,
also because of their ability to trace the solar UV emission. In this work, we
compare the Ca II K 0.1nm emission index to the Mg II index over the time
interval 1978-2017, which covers almost four solar cycles. We show that they
are strongly correlated across each solar cycle (r$\geq$0.94), providing the
corresponding linear regression fit parameters. The Hilbert-Huang Transform is
then used to decompose such indices into their intrinsic mode of oscillation.
By studying how their components are correlated over the different time scales,
it is found that the maximum correlation is observed at the 11-year scale,
while the correlation is less strong going to smaller time scales.
