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We conduct cluster analysis on a class of locally asymptotically self-similarstochastic processes, which includes multifractional Brownian motion as arepresentative. When the true number of clusters is supposed to be known, a newcovariance-based dissimilarity measure is introduced, from which we obtain theapproximately asymptotically consistent clustering algorithms. In simulationstudies, clustering data sampled from multifractional Brownian motions withdistinct functional Hurst parameters illustrates the approximated asymptoticconsistency of the proposed algorithms. Clustering global financial markets'equity indexes returns and sovereign CDS spreads provides a successful realworld application.

Cluster Analysis on Locally Asymptotically Self-similar Processes with Known Number of Clusters