  Permutation Entropy and statistiCal Complexity Analysis for astRophysics
(PECCARY) is a computationally inexpensive, statistical method by which any
time-series can be characterized as predominately regular, complex, or
stochastic. Elements of the PECCARY method have been used in a variety of
physical, biological, economic, and mathematical scenarios, but have not yet
gained traction in the astrophysical community. This study introduces the
PECCARY technique with the specific aims to motivate its use in and optimize it
for the analysis of astrophysical orbital systems. PECCARY works by decomposing
a time-dependent measure, such as the x-coordinate or orbital angular momentum
time-series, into ordinal patterns. Due to its unique approach and statistical
nature, PECCARY is well-suited for detecting preferred and forbidden patterns
(a signature of chaos), even when the chaotic behavior is short-lived or when
working with a relatively short duration time-series or small sets of
time-series data. A variety of examples are used to demonstrate the
capabilities of PECCARY. These include mathematical examples (sine waves,
varieties of noise, sums of sine waves, well-known chaotic functions), a double
pendulum system, and astrophysical tracer particle simulations with potentials
of varying intricacies. Since the adopted timescale used to diagnose a given
time-series can affect the outcome, a method is presented to identify an ideal
sampling scheme, constrained by the overall duration and the natural timescale
of the system. The accompanying PECCARY Python package and its usage are
discussed.
