This paper is devoted to the study of period function planar generic and non-generic turning points. In case (resp. non-generic) a non-degenerate degenerate) center disappears in limit e → 0, where ≥ 0 singular perturbation parameter. We show that, for each > ∼ monotonously increasing has exactly one minimum). The result valid an e-uniform neighborhood also solve part conjecture about uniform u...

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 predictions at a lower dimensional state space than the optimal local ...

This work is concerned with autoregressive prediction of turning points in financial price sequences. Such turning points are critical local extrema points along a series, which mark the start of new swings. Predicting the future time of such turning points or even their early or late identification slightly before or after the fact has useful applications in economics and finance. Building on ...