As the Chinese calendar is soli-lunar, the date of change of sign is the Chinese New Year which is the day of the new Moon (on the Beijing date) between January 21 and February 20.
To calculate this, December 21st is always included in the 11th Chinese lunar month. This 11th month is considered to be the middle of winter. The 12th lunar month is the last of the winter season in China and the following month is the first of spring, the Chinese New Year is celebrated on the first day of this first month of spring.
Fearing for their security and that of China, the Emperors forbade consulting the stars. The dates of February 4th or 5th were then chosen to obey the ban and to mark the beginning of the Chinese year in an almost fixed way.
However, the Emperors wanted to continue to consult the horoscopes of the 111 Stars for their personal use. Since there were no astrologers in China anymore, they brought in astrologers from other countries, mainly from Vietnam.
Chinese signs are also used by other Asian cultures, Vietnamese and Japanese for example. The postal services of several other countries sometimes issue a “Year of…” stamp, but countries unfamiliar with the use of the Chinese lunar calendar assume that the signs change on January 1 of each year.
There is a little trick to easily calculate the new Chinese year: the cycle starts again about every 95 years, so in 1900 the year started on January 31, it started on January 31 also in 1995 (be careful it can vary from 1 to 2 days).
Nevertheless, in the pure Chinese zodiac, i.e. in the system of counting the years by combining the celestial stems and the terrestrial branches with which the animals are associated, the change of sign takes place at the beginning of spring, on the day called lichun, which is on the 4th or 5th of February, when the Sun arrives at 315 degrees of longitude. This so-called Bazi calendar is thus distinct from the Chinese New Year calendar determined by the Purple Mountain Observatory in Nanjing, which thus leaves everyone free to rely on the calendar that suits them according to the psychological resemblance they find in their personal astrological animal.