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.