Nice explanation jcl.
It would be interesting to test what is better, to enter in the valley or in the cross.

"why not simply using the prices and the bollinger bands or the standard deviation as thresholds"
Well... as Ehers describes in the fisher transformation paper. bollinger bands consider that the price follows a gaussian distribution it does not. That´s why he uses the fisher transformation so that it is more realistic when the price move out from the mean.