Theoretical Study of Multiscale Permutation Entropy on Finite-Length Fractional Gaussian Noise

Permutation Entropy has been used as a robust and fast approach to calculate complexity of time series. There have been extensive studies on the properties and behavior of Permutation Entropy on known signals. Similarly, Multiscale Permutation Entropy has been used to analyze the structures at different time scales. Nevertheless, the Permutation Entropy is constrained by signal length, a problem which is accentuated with Multiscaling. We have analyzed the fractional Gaussian noise under a Multiscale Permutation Entropy analysis, taking into account the effect of finite-length signals across all scales. We found the Permutation Entropy value of Fractional Gaussian noise to be invariant to time scale. Nonetheless, a finite-length linear approximation for scale dependency is found as a result solely from the finite-length constrains of the method.