Local prediction of turning points of oscillating time series

TL;DR

This paper introduces a method for predicting the timing and magnitude of oscillation turning points by reconstructing the state space solely from these points, improving efficiency and accuracy over traditional methods.

Contribution

It proposes a novel approach that reconstructs the state space from turning points, enabling more efficient and accurate predictions of oscillating time series.

Findings

Better prediction accuracy for turning points.

Lower-dimensional state space reconstruction.

Confirmed effectiveness on real-world data.

Abstract

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.