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On the equivalence between the kinetic Ising model and discrete autoregressive processes


Campajola, Carlo; Lillo, Fabrizio; Mazzarisi, Piero; Tantari, Daniele (2021). On the equivalence between the kinetic Ising model and discrete autoregressive processes. Journal of Statistical Mechanics: Theory and Experiment, 2021(3):033412.

Abstract

Binary random variables are the building blocks used to describe a large variety of systems, from magnetic spins to financial time series and neuron activity. In statistical physics the kinetic Ising model has been introduced to describe the dynamics of the magnetic moments of a spin lattice, while in time series analysis discrete autoregressive processes have been designed to capture the multivariate dependence structure across binary time series. In this article we provide a rigorous proof of the equivalence between the two models in the range of a unique and invertible map unambiguously linking one model parameters set to the other. Our result finds further justification acknowledging that both models provide maximum entropy distributions of binary time series with given means, auto-correlations, and lagged cross-correlations of order one. We further show that the equivalence between the two models permits to exploit the inference methods originally developed for one model in the inference of the other.

Abstract

Binary random variables are the building blocks used to describe a large variety of systems, from magnetic spins to financial time series and neuron activity. In statistical physics the kinetic Ising model has been introduced to describe the dynamics of the magnetic moments of a spin lattice, while in time series analysis discrete autoregressive processes have been designed to capture the multivariate dependence structure across binary time series. In this article we provide a rigorous proof of the equivalence between the two models in the range of a unique and invertible map unambiguously linking one model parameters set to the other. Our result finds further justification acknowledging that both models provide maximum entropy distributions of binary time series with given means, auto-correlations, and lagged cross-correlations of order one. We further show that the equivalence between the two models permits to exploit the inference methods originally developed for one model in the inference of the other.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
08 Research Priority Programs > Social Networks
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Scope:Discipline-based scholarship (basic research)
Language:English
Date:25 March 2021
Deposited On:02 Feb 2022 07:14
Last Modified:18 Jun 2024 03:35
Publisher:IOP Publishing
ISSN:1742-5468
OA Status:Closed
Publisher DOI:https://doi.org/10.1088/1742-5468/abe946
Related URLs:https://iopscience.iop.org/article/10.1088/1742-5468/abe946 (Publisher)
Other Identification Number:merlin-id:21982