  Permutation Entropy (PE) has been shown to be a useful tool for time series
analysis due to its low computational cost and noise robustness. This has drawn
for its successful application in many fields. Some of these include damage
detection, disease forecasting, and financial volatility analysis. However, to
successfully use PE, an accurate selection of two parameters is needed: the
permutation dimension $n$ and embedding delay $\tau$. These parameters are
often suggested by experts based on a heuristic or by a trial and error
approach. unfortunately, both of these methods can be time-consuming and lead
to inaccurate results. To help combat this issue, in this paper we investigate
multiple schemes for automatically selecting these parameters with only the
corresponding time series as the input. Specifically, we develop a
frequency-domain approach based on the least median of squares and the Fourier
spectrum, as well as extend two existing methods: Permutation Auto-Mutual
Information (PAMI) and Multi-scale Permutation Entropy (MPE) for determining
$\tau$. We then compare our methods as well as current methods in the
literature for obtaining both $\tau$ and $n$ against expert-suggested values in
published works. We show that the success of any method in automatically
generating the correct PE parameters depends on the category of the studied
system. Specifically, for the delay parameter $\tau$, we show that our
frequency approach provides accurate suggestions for periodic systems,
nonlinear difference equations, and ECG/EEG data, while the mutual information
function computed using adaptive partitions provides the most accurate results
for chaotic differential equations. For the permutation dimension $n$, both
False Nearest Neighbors and MPE provide accurate values for $n$ for most of the
systems with $n = 5$ being suitable in most cases.
