Relative cluster entropy for power-law correlated sequences

Abstract

We propose an information-theoretical measure, the \textit{relative cluster entropy} ${\mathcal{D}}_{\mathcal{C}}[P\Vert Q]$, 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.

References in corpus (9)

• Power-law distributions in empirical data
• The Role of Relative Entropy in Quantum Information Theory
• Dissipation: The phase-space perspective
• Thermodynamics as a theory of decision-making with information processing costs
• The thermodynamics of prediction
• Thermodynamics with continuous information flow
• A Kullback-Leibler divergence measure of intermittency: application to turbulence
• Information Measures for Long-Range Correlated Sequences: the Case of the 24 Human Chromosome Sequences
• Thermodynamic aspects of information transfer in complex dynamical systems

Cited by in corpus (1)

• Kullback-Leibler cluster entropy to quantify volatility correlation and risk diversity