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Correspondence between temporal correlations in time series, inverse problems, and the spherical model

Marcaccioli, R; Livan, G; (2020) Correspondence between temporal correlations in time series, inverse problems, and the spherical model. Physical Review E , 102 (1) , Article 012112. 10.1103/PhysRevE.102.012112. Green open access

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Abstract

In this paper we employ methods from statistical mechanics to model temporal correlations in time series. We put forward a methodology based on the maximum entropy principle to generate ensembles of time series constrained to preserve part of the temporal structure of an empirical time series of interest. We show that a constraint on the lag-one autocorrelation can be fully handled analytically and corresponds to the well-known spherical model of a ferromagnet. We then extend such a model to include constraints on more complex temporal correlations by means of perturbation theory, showing that this leads to substantial improvements in capturing the lag-one autocorrelation in the variance. We apply our approach on synthetic data and illustrate how it can be used to formulate expectations on the future values of a data-generating process.

Type: Article
Title: Correspondence between temporal correlations in time series, inverse problems, and the spherical model
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevE.102.012112
Publisher version: https://doi.org/10.1103/PhysRevE.102.012112
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Complex systems, Patterns in complex systems, Time series analysis
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10106084
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