Nonlinear time series analysis for point processes

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This research aimed to propose a practical method for ensuring the embedding to characterize point process data from the viewpoint of nonlinear dynamics. For point process data, the size of time window corresponds to the embedding dimension for a time series sampled at a fixed sampling interval. Thus, I proposed a method to choose the size of time window by using prediction errors. By ensuring the embedding, we enable to apply, to point process data, 4 methods including nonlinear prediction, reconstruction of driving forces, identification of directional couplings, and test of deterministic chaos.