Cluster Analysis on Locally Asymptotically Self-similar Processes with Known Number of Clusters
This work addresses clustering in stochastic processes for applications like financial analysis, but it is incremental as it builds on known methods with a specific assumption on cluster count.
The paper tackled clustering of locally asymptotically self-similar processes, such as multifractional Brownian motion, by introducing a new covariance-based dissimilarity measure and algorithms that are approximately asymptotically consistent when the number of clusters is known, with successful application to financial market data.
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.