Correlation lags give early warning signals of approaching tipping points

Identifying upcoming tipping points from observations is an important challenge in time series analysis with practical applications in many fields of science. Well-known indicators are the increase in spatial and temporal correlations. However, the performance of these indicators depends on the system under study and on the type of approaching bifurcation, and no indicator provides a reliable warning for any system and bifurcation. Here we propose an indicator that simultaneously takes into account information about spatial and temporal correlations. By performing a bivariate analysis of signals recorded in pairs of adjacent spatial points, and analyzing the distribution of lag times that maximize their cross-correlation, we find that the variance of the lag distribution consistently decreases as a bifurcation approaches. We demonstrate the reliability of this indicator using different types of models that present different types of bifurcations, including local bifurcations (transcritical, supercritical and subcritical saddle-node and Hopf bifurcations), and global bifurcations.