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Relative cluster entropy for power-law correlated sequences
by A. Carbone, L. Ponta
Submission summary
| Authors (as registered SciPost users): | Anna Carbone |
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| Preprint Link: | https://arxiv.org/abs/2206.02685v2 (pdf) |
| Date accepted: | Aug. 18, 2022 |
| Date submitted: | Aug. 10, 2022, 10:25 a.m. |
| Submitted by: | Anna Carbone |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Computational |
Abstract
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.
List of changes
Change 2: Notations in Eq. (6) have been improved. For the sake of clarity, Eq. (6) has been split over two lines.
Change 3: Eq. (3) has been moved after Eq. (1) and before Eq. (2). Eq. (3) is now labelled Eq. (2).
Change 4: The arrows in the nine panels of Fig. 3 have been removed. A text linking each colour to the parameter n is now added in the caption.
Change 5: The left hand of equations in Section III are now in “math roman font” instead of "mathcal".
Change 6: The three panels in Fig. 5 have been merged together in one single panel.
Change 7: A short text, clarifying the main motivations of the work, is now included in the Introduction.
Published as SciPost Phys. 13, 076 (2022)