PETROPY - Permutation Entropy

(for MATLAB^®)

General Notes

Permutation entropy provides a simple and robust method to estimate complexity of time series, taking the temporal order of the values into account. Furthermore, permutation entropy can be used to determine embedding parameters or identify couplings between time series. For further instructions please consider the reference given below.

Usage

H = petropy(x,n,tau,method,accu)

`x`	time series (N × 1 or 1 × N vector)
`n`	permutation order
`tau`	time lag/ time lag vector (length = n-1)
`method`	method how to deal with equal values in the series `'noise'` - add small noise to the values in x `'same'` - allow same rank for equal values `'order'` - consider order of appearance (first occurence --> lower rank)
`accu`	maximum number of decimal places in x (only used for method `'noise'`)

H gives the value of the permutation entropy according to H = − ∑(p_j log₂ p_j) (j = 1, …, n).

Example

Consider the time series

x = [6,9,11,12,8,13,5];

The permutation entropy of this time series with a permutation order of 3 and with lag 1 is

H = petropy(x,3,1,'order');
H = 
    1.5219

References

Riedl, M., Müller, A., Wessel, N.: Practical considerations of permutation entropy, Eur. Phys. J. ST, 222(2), 249-262, 2013.

Download

petropy.m

Author

Andreas Müller

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University of Potsdam, Interdisciplinary Center for Dynamics of Complex Systems, Germany
Potsdam Institute for Climate Impact Research, Complexity Science, Germany
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