The Economist's Johnson Blog (named after the great dictionary pioneer) confidently put forward a theory last year - only to quickly withdraw it after protests from commentators. I personally go with the idea Peking is the Cantonese form of the word. This is what I was told when I lived in (Cantonese speaking) Hong Kong and seems to make sense.
Anyway, Kung Hei Fat Choi (a Happy (Cantonese!) New Year