A method is proposed for determining the time interval at which a significant change in the ratio of the amplitudes of the Chandler and annual components of the Earth's pole motion (the point of intersection of the instantaneous Earth's rotation axis with the Earth's surface) occurs. So for several decades one model or a family of forecasting models can work successfully, but when the amplitude ratio changes, they become inapplicable and other models should be taken that are more consistent to the new movement. The result is used to refine the model of the Earth's rotation and to select a strategy for predicting the pole position, whose oscillation due to the atmosphere and the ocean circulation is non-linear.