Counting forbidden patterns in irregularly sampled time series. I. The effects of under-sampling, random depletion, and timing jitter.

It has been established that the count of ordinal patterns, which do not occur in a time series, called forbidden patterns, is an effective measure for the detection of determinism in noisy data. A very recent study has shown that this measure is also partially robust against the effects of irregular sampling. In this paper, we extend said research with an emphasis on exploring the parameter space for the method's sole parameter-the length of the ordinal patterns-and find that the measure is more robust to under-sampling and irregular sampling than previously reported. Using numerically generated data from the Lorenz system and the hyper-chaotic Rössler system, we investigate the reliability of the relative proportion of ordinal patterns in periodic and chaotic time series for various degrees of under-sampling, random depletion of data, and timing jitter. Discussion and interpretation of results focus on determining the limitations of the measure with respect to optimal parameter selection, the quantity of data available, the sampling period, and the Lyapunov and de-correlation times of the system.