  The re-emission in the cores of the Ca II H & K and H$\alpha$ lines, are well
known proxies of stellar activity. However, these activity indices probe
different activity phenomena, the first being more sensitive to plage
variation, while the other one being more sensitive to filaments. In this paper
we study the long-term correlation between $\log R'_{HK}$ and $\log
I_{H\alpha}$, two indices based on the Ca II H & K and H$\alpha$ lines
respectively, for a sample of 271 FGK stars using measurements obtained over a
$\sim$9 year time span. Because stellar activity is one of the main obstacles
to the detection of low-mass and long-period planets, understanding further
this activity index correlation can give us some hints about the optimal target
to focus on, and ways to correct for these activity effects. We found a great
variety of long-term correlations between $\log R'_{HK}$ and $\log
I_{H\alpha}$. Around 20% of our sample has strong positive correlation between
the indices while about 3% show strong negative correlation. These fractions
are compatible with those found for the case of early-M dwarfs. Stars
exhibiting a positive correlation have a tendency to be more active when
compared to the median of the sample, while stars showing a negative
correlation are more present among higher metallicity stars. There is also a
tendency for the positively correlated stars to be more present among the
coolest stars, a result which is probably due to the activity level effect on
the correlation. Activity level and metallicity seem therefore to be playing a
role on the correlation between $\log R'_{HK}$ and $\log I_{H\alpha}$. Possible
explanations based on the influence of filaments for the diversity in the
correlations between these indices are discussed in this paper.
