Hodrick-Prescott issue

I'm building a Leading Indicator for the economic cycle similar to the OECD's (http://www.oecd.org/std/leading-indicators/), so I use Hodrick-Prescott to filter the series. I know that with this filter the series is recalculated as new data are published.
The thing is that, when a peak/trough occurs, the series shows a particular behavior (as you can see in the graph attached) - that is, for the first couple of months it does not recognize the change in the economic cycle, and after that there is a huge revision.
So, I'd like to know why does it happen: I believe that it is related to the fact that it takes at least a couple of month to the algorithm to detect the beginning/end of an economic cycle, but I am not sure about it.
Thank you!