Geodesic
Determination of phase-space reconstruction parameters of chaotic time series
Kybernetika, Tome 44 (2008) no. 4, pp. 557-570 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A new method called C-C-1 method is suggested, which can improve some drawbacks of the original C-C method. Based on the theory of period N, a new quantity S(t) for estimating the delay time window of a chaotic time series is given via direct computing a time-series quantity S(m,N,r,t), from which the delay time window can be found. The optimal delay time window is taken as the first period of the chaotic time series with a local minimum of S(t). Only the first local minimum of the average of a quantity Δ S2(t) is needed to ascertain the optimal delay time. The parameter of the C-C method - embedding dimension $m$ - is adjusted rationally. In the new method, the estimates of the optimal delay time and the optimal delay time window are more appropriate. The robustness of the C-C-1 method reaches 40
A new method called C-C-1 method is suggested, which can improve some drawbacks of the original C-C method. Based on the theory of period N, a new quantity S(t) for estimating the delay time window of a chaotic time series is given via direct computing a time-series quantity S(m,N,r,t), from which the delay time window can be found. The optimal delay time window is taken as the first period of the chaotic time series with a local minimum of S(t). Only the first local minimum of the average of a quantity Δ S2(t) is needed to ascertain the optimal delay time. The parameter of the C-C method - embedding dimension $m$ - is adjusted rationally. In the new method, the estimates of the optimal delay time and the optimal delay time window are more appropriate. The robustness of the C-C-1 method reaches 40
Classification : 37D45, 37M10, 62M10, 62M15
Keywords: phase-space reconstruction; embedding window; delay time; time series 
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     title = {Determination of phase-space reconstruction parameters of chaotic time series},
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Cai, Wei-Dong; Qin, Yi-Qing; Yang, Bing-Ru. Determination of phase-space reconstruction parameters of chaotic time series. Kybernetika, Tome 44 (2008) no. 4, pp. 557-570. http://geodesic.mathdoc.fr/item/KYB_2008_44_4_a10/

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