  For oscillating time series, the prediction is often focused on the turning
points. In order to predict the turning point magnitudes and times it is
proposed to form the state space reconstruction only from the turning points
and modify the local (nearest neighbor) model accordingly. The model on turning
points gives optimal prediction at a lower dimensional state space than the
optimal local model applied directly on the oscillating time series and is thus
computationally more efficient. Monte Carlo simulations on different
oscillating nonlinear systems showed that it gives better predictions of
turning points and this is confirmed also for the time series of annual
sunspots and total stress in a plastic deformation experiment.
