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On the equivalence between the Kinetic Ising Model and discrete autoregressive processes

Carlo Campajola, Fabrizio Lillo, Piero Mazzarisi, Daniele Tantari

arXiv 24 Aug 2020 · cond-mat.stat-mech · 9 citations (OpenAlex)

arXiv:2008.10666 · PDF · OpenAlex · Extracted main text

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.

Citation extraction

41
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distinct cited
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main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Piero Mazzarisi, Silvia Zaoli, Carlo Campajola, and Fabrizio Lillo (2020) Tail granger causalities and where to find them: Extreme risk spillovers vs spurious linkages self0.73732100%
2Carlo Campajola, Domenico Di Gangi, Fabrizio Lillo, and Daniele Tant… (2020) Modelling time-varying interactions in complex systems: the Score Driven Kinetic Ising Model self0.64422100%
3A Crisanti and Haim Sompolinsky (1988) Dynamics of spin systems with randomly asymmetric bonds: Ising spins and Glauber dynamics0.64422100%
4Glenn H Fredrickson and Hans C Andersen (1984) Kinetic Ising model of the glass transition0.51121100%
5Patricia A Jacobs and Peter AW Lewis (1978) Discrete time series generated by mixtures. III. autoregressive processes (DAR (p))0.51121100%
6Patricia A Jacobs and Peter AW Lewis (1983) Stationary discrete autoregressive-moving average time series generated by mixtures0.51121100%
7Edwin T Jaynes (1957) Information theory and statistical mechanics0.51121100%
8Marc Mézard and J Sakellariou (2011) Exact mean-field inference in asymmetric kinetic ising systems0.51121100%
9Lionel Barnett, Joseph T Lizier, Michael Harré, Anil K Seth, and Ter… (2013) Information flow in a kinetic Ising model peaks in the disordered phase0.40511100%
10Jean-Philippe Bouchaud, Marc Mézard, Marc Potters, et al (2002) Statistical properties of stock order books: empirical results and models0.40511100%

Showing the top 10 of 41 scored citations.