TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.13.3.076
TI  - Relative cluster entropy for power-law correlated sequences
PY  - 2022/09/30
UR  - https://scipost.org/SciPostPhys.13.3.076
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 13
IS  - 3
SP  - 076
A1  - Carbone, Anna
AU  - Ponta, Linda
AB  - We propose an information-theoretical measure, the \textit{relative cluster entropy} $\mathcal{D_{C}}[P \| Q] $, to discriminate among cluster partitions characterised by probability distribution functions $P$ and $Q$. The measure is illustrated with the clusters generated by pairs of fractional Brownian motions with Hurst exponents $H_1$ and $H_2$ respectively. For subdiffusive, normal and superdiffusive sequences, the relative entropy sensibly depends on the difference between $H_1$ and $H_2$. By using the \textit{minimum relative entropy} principle, cluster sequences characterized by different correlation degrees are distinguished and the optimal Hurst exponent is selected. As a case study, real-world cluster partitions of market price series are compared to those obtained from fully uncorrelated sequences (simple Browniam motions) assumed as a model. The \textit{minimum relative cluster entropy} yields optimal Hurst exponents $H_1=0.55$, $H_1=0.57$, and $H_1=0.63$ respectively for the prices of DJIA, S\&P500, NASDAQ: a clear indication of non-markovianity. Finally, we derive the analytical expression of the relative cluster entropy and the outcomes are discussed for arbitrary pairs of power-laws probability distribution functions of continuous random variables.
ER  -

@Article{10.21468/SciPostPhys.13.3.076,
	title={{Relative cluster entropy for power-law correlated sequences}},
	author={Anna Carbone and Linda Ponta},
	journal={SciPost Phys.},
	volume={13},
	pages={076},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.13.3.076},
	url={https://scipost.org/10.21468/SciPostPhys.13.3.076},
}