Series Representation of Jointly S$$\alpha $$S Distribution via Symmetric Covariations

Ding, Yujia; Peng, Qidi

doi:10.1007/s40304-020-00216-5

Cited by 1 publication

(1 citation statement)

References 34 publications

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“…Cluster analysis of such stable processes will no doubt lead to a wide range of applications, especially when the process distributions exhibit heavy-tailed phenomena. Neither the distribution dissimilarity measure introduced in [12] nor the covariance-based dissimilarity measures used in this paper would work in this case, hence new techniques are required to cluster such processes, such as considering replacing the covariances with covariations [35] or symmetric covariations [57] in the dissimilarity measures.…”

Section: Conclusion and Future Prospectsmentioning

confidence: 99%

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

2022

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We conduct cluster analysis of a class of locally asymptotically self-similar stochastic processes with finite covariance structures, which includes Brownian motion, fractional Brownian motion, and multifractional Brownian motion as paradigmatic examples. Given the true number of clusters, a new covariance-based dissimilarity measure is introduced, based on which we obtain approximately asymptotically consistent algorithms for clustering locally asymptotically self-similar stochastic processes. In the simulation study, clustering data sampled from fractional and multifractional Brownian motions with distinct 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. Implementations in MATLAB of the proposed algorithms and the simulation study are publicly shared in GitHub.

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Section: Conclusion and Future Prospectsmentioning

confidence: 99%