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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.
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data. Here we inv
An important problem in statistical physics concerns the fascinating connections between partition functions of lattice models studied in equilibrium statistical mechanics on the one hand and graph theoretical enumeration problems on the other hand.
Recent observation studies have revealed that earthquakes are classified into several different categories. Each category might be characterized by the unique statistical feature in the time series, but the present understanding is still limited due
The problem of the equivalence of the spherical and mean spherical models, which has been thoroughly studied and understood in equilibrium, is considered anew from the dynamical point of view during the time evolution following a quench from above to
We study roughness probability distribution functions (PDFs) of the time signal for a critical interface model, which is known to provide a good description of Barkhausen noise in soft ferromagnets. Starting with time ``windows of data collection muc