  We aim to explore the variable photometric and stellar properties of four
yellow hypergiants (YHGs), HR8752, HR 5171A, $\rho$ Cas, and HD 179821, and
their pulsations of hundreds of days, and long-term variations (LTVs) of years.
We tackled multi-colour and visual photometric data sets, looked for
photometric indications betraying eruptions or enhanced mass-loss episodes,
calculated stellar properties mainly using a published temperature calibration,
and investigated the nature of LTVs and their influence on quasi-periods and
stellar properties. The $BV$ photometry revealed a high-opacity layer in the
atmospheres. When the temperature rises the mass loss increases as well,
consequently, as the density of the high-opacity layer. As a result, the
absorption in $B$ and $V$ grow. The absorption in $B$, presumably of the order
of one to a few 0\fm1, is always higher than in $V$. This difference renders
redder and variable $(B-V)$ colour indexes, but the absorption law is unknown.
This property of YHGs is unpredictable and explains why spectroscopic
temperatures are always higher than photometric ones. We propose shorter
distances for $\rho$ Cas and HR 5171A than the accepted ones. Therefore, a
correction to decrease the blue luminescence of HR 5171A by polycyclic aromatic
hydrocarbon (PAH) molecules is necessary, and HR 5171A would no longer be a
member of the cluster Gum48d. HR 5171A is only subject to one source of light
variation, not by two as the literature suggests. Eruptive episodes of YHGs
prefer relatively cool circumstances when a red evolutionary loop (RL) has
shifted the star to the red on the HR diagram. After the eruption, a blue loop
evolution (BL) is triggered lasting one to a few decades. The reddening episode
of HR 5171A between 1960 and 1974 was most likely due to a red loop evolution,
and the reddening after the 1975 eruption was likely due to a shell ejection.

Solar and Stellar Astrophysics