Statistical early-warning indicators based on autoregressive moving-average models

We address the problem of defining early-warning indicators of critical transitions. To this purpose, we fit the relevant time series through a class of linear models, known as autoregressive 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-neighbor interaction. We then apply the method to complex systems, namely for dynamo thresholds and financial crisis detection.