Fig. 3
From: Modeling and inference of mixed dynamics and detection of causal emergent features
Forecasting with the ALM model: One advantage of this approach is that the model is able to self-evaluate its residual fit on a running basis. Should the residual, assumed to be Normal, accumulate sufficient skewness, the model can form a model selection test to include a hypothesis that a change-point has recently occurred. By comparing the current model (e.g., in (a) having two causes for growth), to an alternate model which posits an additional generating process (e.g., in (b) a third cause is introduced). Change to the model is accepted if the model improvements (correction for skewness or to improve the residual) outweigh the cost for adding an additional component imposed by the regularization term. This can be efficiently automated and performed by the model on a recurring basis. New dynamic regimes can be identified shortly after evidence mounts that data diverges from the current best forecast model.
