Statistical early-warning indicators based on Auto-Regressive   Moving-Average processes
  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. 
Davide Faranda and Flavio Maria Emanuele Pons and B\'ereng\`ere   Dubrulle
physics.data-an nlin.CD