Relative cluster entropy for power-law correlated sequences

We propose an information-theoretical measure, the relative cluster entropy \mathcal{D_C}[P\|Q] [ 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 mot...

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Vydáno v:SciPost physics Ročník 13; číslo 3; s. 076
Hlavní autoři: Carbone, Anna, Ponta, Linda
Médium: Journal Article
Jazyk:angličtina
Vydáno: SciPost 01.09.2022
ISSN:2542-4653, 2542-4653
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Abstract We propose an information-theoretical measure, the relative cluster entropy \mathcal{D_C}[P\|Q] [ 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 H 1 and H_2 H 2 respectively. For subdiffusive, normal and superdiffusive sequences, the relative entropy sensibly depends on the difference between H_1 H 1 and H_2 H 2 . By using the 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 minimum relative cluster entropy yields optimal Hurst exponents H_1 H 1 =0.55, H_1 H 1 =0.57, and H_1 H 1 =0.63 respectively for the prices of DJIA, S and 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.
AbstractList 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.
We propose an information-theoretical measure, the relative cluster entropy \mathcal{D_C}[P\|Q] [ 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 H 1 and H_2 H 2 respectively. For subdiffusive, normal and superdiffusive sequences, the relative entropy sensibly depends on the difference between H_1 H 1 and H_2 H 2 . By using the 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 minimum relative cluster entropy yields optimal Hurst exponents H_1 H 1 =0.55, H_1 H 1 =0.57, and H_1 H 1 =0.63 respectively for the prices of DJIA, S and 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.
ArticleNumber 076
Author Carbone, Anna
Ponta, Linda
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CitedBy_id crossref_primary_10_1016_j_patrec_2025_03_004
crossref_primary_10_1016_j_cnsns_2024_108469
crossref_primary_10_1103_PhysRevE_111_014311
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10.1103/RevModPhys.74.197
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