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

TL;DR

This paper introduces a covariance-based dissimilarity measure for clustering locally asymptotically self-similar stochastic processes, demonstrating asymptotic consistency through simulations and real-world financial data applications.

Contribution

A novel covariance-based dissimilarity measure enabling consistent clustering of locally asymptotically self-similar processes with known number of clusters.

Findings

Algorithms show asymptotic consistency in simulations.

Successful clustering of financial market data.

Effective application to real-world financial datasets.

Abstract

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.