State space reconstruction parameters in the analysis of chaotic time series - The role of the time window length
State space reconstruction parameters in the analysis of chaotic time series - The role of the time window length
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DOI：
10.1016/0167-2789(96)00054-1
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发表时间：
1996-08-01
期刊：
影响因子：
4
通讯作者：
Kugiumtzis, D
中科院分区：
文献类型：
--
作者：
Kugiumtzis, D
在混沌时间序列分析中，最常用的状态空间重构方法是延迟法（MOD）。已经提出了许多技术来估计MOD的参数，即时间延迟τ和嵌入维数rn。我们讨论了这些技术的适用性与批判性的观点，其有效性，并指出确定的整体时间窗口长度，τ（w），成功嵌入的必要性。重点放在τ（w）和潜在的混沌系统的动力学之间的关系，我们建议设置τ（w）大于或等于τ（p），平均轨道周期; τ（p）是近似的振荡的时间序列。该程序是使用合成和真实的数据的关联维数进行评估。对于干净的合成数据，在给定足够的数据的情况下，大于tau（p）的tau（w）的值总是给出良好的结果，因此tau（p）可以被认为是下限（tau（w）大于或等于tau（p））。对于有噪声的合成数据和真实的数据，τ（w）达到上限，其接近τ（p）以增加噪声幅度。
The most common state space reconstruction method in the analysis of chaotic time series is the Method of Delays (MOD). Many techniques have been suggested to estimate the parameters of MOD, i.e. the time delay tau and the embedding dimension rn. We discuss the applicability of these techniques with a critical view as to their validity, and point out the necessity of determining the overall time window length, tau(w), for successful embedding. Emphasis is put on the relation between tau(w) and the dynamics of the underlying chaotic system, and we suggest to set tau(w) greater than or equal to tau(p), the mean orbital period; tau(p) is approximated from the oscillations of the time series. The procedure is assessed using the correlation dimension for both synthetic and real data. For clean synthetic data, values of tau(w) larger than tau(p) always give good results given enough data and thus tau(p) can be considered as a lower limit (tau(w) greater than or equal to tau(p)). For noisy synthetic data and real data, an upper limit is reached for tau(w) which approaches tau(p) for increasing noise amplitude.