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

We conduct cluster analysis of a class locally asymptotically self-similar stochastic processes with finite covariance structures, which includes Brownian motion, fractional and multifractional motion as paradigmatic examples. Given the true number clusters, new covariance-based dissimilarity measure is introduced, based on we obtain approximately consistent algorithms for clustering processes. In simulation study, data sampled from motions distinct Hurst parameters illustrates approximated asymptotic consistency proposed algorithms. Clustering global financial markets’ equity indexes returns sovereign CDS spreads provides successful real world application. Implementations in MATLAB study are publicly shared GitHub.