Mean local autocovariance provides robust and versatile choice of delay for reconstruction using frequently sampled flowlike data

The first step in nonlinear time-series analysis can be selecting a delay for reconstruction. The most popular choices of this delay are the first zero of the autocovariance and the first minimum of the mutual information. An advantage of the first method arises from the robustness to noise of the autocovariance function, while an advantage of the second is that the first minimum of the mutual information provides a useful choice of delay for a wide range of nonlinear systems. We propose a method to choose a delay for frequently sampled flowlike data based on a mean local autocovariance function and compare its performance to methods based on the autocovariance and the mutual information. In addition, we compare the novel method to an established method based on cross-validatory mean-square errors of predictors corresponding to different choices of delay. The mean local autocovariance combines the versatility of the mutual information with some of the robustness to noise of the autocovariance.