if its feathers are looking rough, maybe its had a runin with a cat or kids? Its also a tame bird so is used to be cared for, and may need help I would imagine. I really wouldn't think it would survive for long without help, and is very unlikey to get through the looming winter 
I've googled, and the info I found said even champion birds may get lost occasionally and need help, it advises you hopw to identify it, offers help on getting it back home, and advises on how to care for it.
http://www.homingpigeons.co.uk/straypigeons.htm
Good luck, as its been there for 2 days I would def try and catch it to get the details from it.
My light may be on, but that doesn't always mean I am looking at the PC - I am far more likely to be cuddling or feeding Tianna atm, so please don't think I am ignoring you if I don't reply quickly
Our Precious Baby Tianna has now joined our Family, she is much loved and very welcome, xxx
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