Conjecture, omen, prophecy, augury...
Sure, a synonym for "auspices" could be "patronage" or "support."
An augury is a divination based on the appearance and behaviour of animals, or, by extension, any omen or prediction.
If you mean "prediction gov", it is the official government weather prediction website.
omen
good or bad
an omen or prophecy
No, an omen is a sign, which can mean good, bad, dangerous, etc. And a warning is something that is going to happen. For example the clouds are dark grey, that is a warning that a storm is coming. A omen is something religious and can be and mean different things to different people.
It is a bad omen
to blurtit out
Under favorable omen
the foretelling or prediction of what is to come.