  We address the problem of defining early warning indicators of critical
transition. To this purpose, we fit the relevant time series through a class of
linear models, known as Auto-Regressive Moving-Average (ARMA(p,q)) models. We
define two indicators representing the total order and the total persistence of
the process, linked, respectively, to the shape and to the characteristic decay
time of the autocorrelation function of the process. We successfully test the
method to detect transitions in a Langevin model and a 2D Ising model with
nearest-neighbour interaction. We then apply the method to complex systems,
namely for dynamo thresholds and financial crisis detection.
