I am not sure I am completely following. My thoughts:
- Your data seems to be really short. This is a problem with the HP filter. See e.g. Limited number of observations - #2 by jpfeifer
- I am not sure that correlations in such a short sample are really meaningful. It’s not even a full cycle.
- Standard deviations in percent are (approximately) the standard deviations of the logged cyclical values. Once you have taken the log, any division by the mean is wrong. When using the HP filter on logged values, you will be getting percentage deviations from trend, which is already what you want.
- The cyclical component indeed looks extremely smooth, but the problem mostly seems to be with the original data, which looks like it has already been filtered. There is not much high-frequency movement.