Equilibrium-mean shifts can result from changes in intercepts with constant dynamics, or be induced by shifts in dynamics with non-zero data means, or both. Induced shifts distort parameter estimates and create a discrepancy between the forecast origin and the equilibrium mean, leading to forecast failure and requiring modifications to previous forecast-error taxonomies. Step-indicator saturation can detect induced shifts, but that does not correct forecast failure. To discriminate direct from induced equilibrium-mean shifts, we augment the model by multiplicative indicators where all selected step indicators interact with the lagged regressand. Forecasts can be markedly improved after induced shifts by including these interactive indicators.
Castle, J.L., Doornik, J.A. & Hendry, D.F. (2023), 'Improving models and forecasts after equilibrium-mean shifts', International Journal of Forecasting.