  Dynamic networks exhibit temporal patterns that vary across different time
scales, all of which can potentially affect processes that take place on the
network. However, most data-driven approaches used to model time-varying
networks attempt to capture only a single characteristic time scale in
isolation --- typically associated with the short-time memory of a Markov chain
or with long-time abrupt changes caused by external or systemic events. Here we
propose a unified approach to model both aspects simultaneously, detecting
short and long-time behaviors of temporal networks. We do so by developing an
arbitrary-order mixed Markov model with change points, and using a
nonparametric Bayesian formulation that allows the Markov order and the
position of change points to be determined from data without overfitting. In
addition, we evaluate the quality of the multiscale model in its capacity to
reproduce the spreading of epidemics on the temporal network, and we show that
describing multiple time scales simultaneously has a synergistic effect, where
statistically significant features are uncovered that otherwise would remain
hidden by treating each time scale independently.
