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Relative cluster entropy for power-law correlated sequences
by A. Carbone, L. Ponta
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Submission summary
Authors (as registered SciPost users): | Anna Carbone |
Submission information | |
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Preprint Link: | https://arxiv.org/abs/2206.02685v2 (pdf) |
Date accepted: | 2022-08-18 |
Date submitted: | 2022-08-10 10:25 |
Submitted by: | Carbone, Anna |
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} DC[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 H1 and H2 respectively. For subdiffusive, normal and superdiffusive sequences, the relative entropy sensibly depends on the difference between H1 and H2. 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 H1=0.55, H1=0.57, and H1=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 1: A short text clarifying the meaning of the approach and its relation with the coarse-grained is now added in the Introduction.
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)