  The aim of this paper is to introduce the Lempel-Ziv permutation complexity
vs permutation entropy plane as a tool to analyze time series of different
nature. This two quantities make use of the Bandt and Pompe representation to
quantify continuous-state time series. The strength of this plane is to combine
two different perspectives to analyze a signal, one being statistic (the
permutation entropy) and the other being deterministic (the Lempel-Ziv
complexity). This representation is applied (i) to characterize non-linear
chaotic maps, (ii) to distinguish deterministic from stochastic processes and
(iii) to analyze and differentiate fractional Brownian motion from fractional
Gaussian noise and K-noise given a same (averaged) spectrum. The results allow
to conclude that this plane is "robust" to distinguish chaotic signals from
random signals, as well as to discriminate between different Gaussian and
nonGaussian noises.
