Hi,

with
     $ date -r test
I get:
     Di 10. Jan 22:39:14 CET 2017
but with
     $ date -d "$(($(date -r test +%s)-$(date +%s))) seconds -2 months"
I get:
    Sa 12. Nov 22:39:14 CET 2016

I think the better result would be according to a calculation order from 
left to right:
    Sa 10. Nov 22:39:14 CET 2016

Otherwise it seems impossible to correctly change the time stamp of a 
file relative to its current value.
Example:
     $ touch -t $(date -d "$(($(date -r test +%s)-$(date +%s))) seconds 
-2 months" +%Y%m%d%H%M.%S) test
Additionally the command is not correctly reversible with:
     $ touch -t $(date -d "$(($(date -r test +%s)-$(date +%s))) seconds 
+2 months" +%Y%m%d%H%M.%S) test

Regards
Ulf