Model-based leading indicators for critical transitions
In a recent work with Tony Ives, we showed how modified linear models with time-varying parameters can be used to extract an indicator of instability for a time series that may be drifting towards a regime shift. The paper is available online in Ecosphere. The idea is simply that instead of fitting an autoregressive model and finding a fixed value for its parameters, to fit an autoregressive model with parameters that change based on the point one is along the time series. This is possible due to a Kalman filter fitting proceedure and seems to not require a too much long time series. We also show that fitting threshold autoregressive models can distinguish alternative attractors in a flickering time series. The code to execute all this is currently in Matlab, but we aim in converting it to an easy to use routine in the R environment.