There is no clear candidate for a common ancestor, either in living forms descended from that ancestor, or in fossil forms. Since the skeletal system is so different, the ancestor probably did not have any kind of skeletal system (which would make finding a fossil ancestor unlikely).
Arthropods and vertebrates both share a segmented body plan (less obviously in vertebrates, but it can be seen in primitive chordates like Amphioxus). The development of segmentation is governed by similar genes, suggesting that the ancestor of both may also have been segmented. However, the actual process of the development of segmentation differs, so that it is possible it arose independently in both groups.
