Context. The recent detection of warm H$_2$O vapor emission from the outflows of carbon-rich asymptotic giant branch (AGB) stars challenges the current understanding of circumstellar chemistry. Two mechanisms have been invoked to explain warm H$_2$O vapor formation. In the first, periodic shocks passing through the medium immediately above the stellar surface lead to H$_2$O formation. In the second, penetration of ultraviolet interstellar radiation through a clumpy circumstellar medium leads to the formation of H$_2$O molecules in the intermediate wind. Aims. We aim to determine the properties of H$_2$O emission for a sample of 18 carbon-rich AGB stars and subsequently constrain which of the above mechanisms provides the most likely warm H$_2$O formation pathway. Methods, Results, and Conclusions. See paper.