J. Japan Statist. Soc., Vol. 31 (No. 1), pp. 27-38, 2001

Estimating the Embedding Dimension and Delay Time from Chaotic Time Series with Dynamic Noise

Kaoru Fueda and Takashi Yanagawa

Abstract. This paper considers the chaotic time series with additive dynamic noise. Defining the embedding dimension and delay time, we discuss their mathematical properties. A method of estimating the embedding dimension and delay time is proposed, and the consistency of the estimators is proved.

Key words and phrases: Chaotic time series, non-linear autoregressive model, embedding dimension, delay time, cross-validation.

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