  We conduct cluster analysis on a class of locally asymptotically self-similar
stochastic processes, which includes multifractional Brownian motion as a
representative. When the true number of clusters is supposed to be known, a new
covariance-based dissimilarity measure is introduced, from which we obtain the
approximately asymptotically consistent clustering algorithms. In simulation
studies, clustering data sampled from multifractional Brownian motions with
distinct functional Hurst parameters illustrates the approximated asymptotic
consistency of the proposed algorithms. Clustering global financial markets'
equity indexes returns and sovereign CDS spreads provides a successful real
world application.
