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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| Veröffentlicht in: | SciPost physics Jg. 13; H. 3; S. 076 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
SciPost
01.09.2022
|
| ISSN: | 2542-4653, 2542-4653 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| ISSN: | 2542-4653 2542-4653 |
| DOI: | 10.21468/SciPostPhys.13.3.076 |