Early warnings of unknown nonlinear shifts: a nonparametric approach.

Early warning signals (EWS) of regime shifts are challenging in cases where the true natural data-generating process is uncertain. Nonparametric drift-diffusion-jump models address this problem by fitting a general model that can approximate a wide range of data-generating processes. Drift measures the local rate of change. Diffusion measures relatively small shocks that occur at each time step. Jumps are large intermittent shocks. Total variance combines the contributions of diffusion and jumps. Nonparametric methods are well suited to emerging technology for automated, high-frequency sensors. Total variance is the most precisely measured indicator. Jump intensity appears to be a useful EWS. Estimates of the drift are highly uncertain unless long time series with many regime shifts are available. EWS computed from drift estimates (such as autocorrelation coefficients or return rates) have low precision and should be used with caution. Nonetheless, in the current state of knowledge, it is premature to disregard any potential EWS.

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