  In this paper, we define finite type invariants for cyclic equivalence
classes of nanophrases and construct the universal ones. Also, we identify the
universal finite type invariant of degree 1 essentially with the linking
matrix. It is known that extended Arnold's basic invariants to signed words are
finite type invariants of degree 2, by Fujiwara. We give another proof of this
result and show that those invariants do not provide the universal one of
degree 2.
