Cayo's brother, Pedro, told us that the Ecuadorean custom of burning Ano Viejo figures on New Years Eve originated many years ago with a malaria epidemic near the coast. Apparently, in an effort to contain the epidemic, the citizens in the affected areas were asked to burn their clothing and household linens. This coincided with the end of the year and the connection was quickly made, that the burning could represent an end to the ills of the old year and a clean beginning for the new. Over time the custom continued and evolved into the figures representing the old year.
I don't know if this story is true, but sounds plausible. (though I don't know that burning the clothing would have any effect on the spread of malaria) It does seem that this is a uniquely Ecuadorean custom. I love the idea and found it both fun and festive and, at some level, contemplative and quite cathartic.