The Chinese astrological signs are a little different than their western counterparts.
The Chinese lunar calendar has a sixty year cycle, where the basic five elements, namely:
Metal, Water, Wood, Fire and Earth
are combined with the twelve animal signs of:
Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Lamb, Monkey, Rooster, Dog and Pig
to give a sixty year lunar cycle.
Your sign is taken from which year you were born in, as opposed to what part of the year you were born in.