  The solar activity displays variability and periodic behaviours over a wide
range of timescales, with the presence of a most prominent cycle with a mean
length of 11 years. Such variability is transported within the heliosphere by
solar wind, radiation and other processes, affecting the properties of the
interplanetary medium. The presence of solar activity-related periodicities is
well visible in different solar wind and geomagnetic indices, although with
time lags with respect to the solar one, leading to hysteresis cycles. Here, we
investigate the time lag behaviour between a physical proxy of the solar
activity, the Ca II K index, and two solar wind parameters (speed and dynamic
pressure), studying how their pairwise relative lags vary over almost five
solar cycles. We find that the lag between Ca II K index and solar wind speed
is not constant over the whole time interval investigated, with values ranging
from 6 years to 1 year (average 3.2 years). A similar behaviour is found also
for the solar wind dynamic pressure. Then, by using a Lomb-Scargle periodogram
analysis we obtain a 10.21-year mean periodicity for the speed and 10.30-year
for the dynamic pressure. We speculate that the different periodicities of the
solar wind parameters with respect to the solar 11-year cycle may be related to
the overall observed temporal evolution of the time lags. Finally, by
accounting for them, we obtain empirical relations that link the amplitude of
the Ca II K index to the two solar wind parameters.
