The natural weathering process of oxidation occurred on the copper plating used on the outside of the Statue of Liberty, creating a layer of green colored patina. This is mainly why the Statue of Liberty is green.
When the statue was first put together, it had a dull brown color that reflects the color of the natural copper plating used. It seems like the statue remained this color until around 1920, by this time it had completely changed color because of hundreds of thin sheets of copper it was made out of, as the metal became oxidized by a combination of air and water, it turned green.
However, because of how the plating was layered, the statue of liberty actually moves with changes in temperature and wind speed. Some people were worried that this green patina was actually damaging or signaling low maintenance of the Statue of Liberty that was an essential symbol of our country, but the patina actually protects the copper that lies underneath from further weathering.