Abstract:

The determinism of time series has a direct impact on the choice of the theoretical framework. A method to detect the determinism of nonlinear time series is proposed. This method first reconstructs the time series into a high dimensional space. Then the low-dimensional projector of the high-dimensional manifolds is found in a lowdimensional Euclidean space. When the projector is reflected back to the high-dimensional space, there are differences between the projector and the high-dimensional manifolds. By comparing the high-dimensional manifolds and the projector reflected back to the high-dimensional space, the determinism of the time series can be detected. The simulation results show that the method is reliable.