The most common state space reconstruction method in the analysis of chaotictime series is the Method of Delays (MOD). Many techniques have been suggestedto estimate the parameters of MOD, i.e. the time delay $\tau$ and the embeddingdimension $m$. We discuss the applicability of these techniques with a criticalview as to their validity, and point out the necessity of determining theoverall time window length, $\tau_w$, for successful embedding. Emphasis is puton the relation between $\tau_w$ and the dynamics of the underlying chaoticsystem, and we suggest to set $\tau_w \geq \tau_p$, the mean orbital period;$\tau_p$ is approximated from the oscillations of the time series. Theprocedure is assessed using the correlation dimension for both synthetic andreal 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 consideredas a lower limit ($\tau_w \geq \tau_p$). For noisy synthetic data and realdata, an upper limit is reached for $\tau_w$ which approaches $\tau_p$ forincreasing noise amplitude.
展开▼
