  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.
