global_complexity function

A function to compute global information and complexity measures for time series

This is a high-level function that calculates global complexity measures directly from a given time series or ordinal pattern distribution.

global_complexity(x = NA, opd = NA, ndemb)

Arguments

• x: (OPTIONAL) If opd is not specified, a time series vector x must be specified
• opd: A numeric vector that details an ordinal pattern distribution in a user-specified permutation coding scheme.
• ndemb: (OPTIONAL) If x is given, the embedding dimension (ndemb) is required.

Returns

A named vector containing the three global complexity measures.

Details

This function calculates the following global measures of complexity and information:

• Permutation Entropy (PE, cf. Bandt and Pompe, 2002)
• Permutation Statistical complexity (MPR complexity, cf. Martin, Plastino and Rosso, 2006)
• Number of "forbiden patterns" (cf. Amigo 2010)

Examples

x = arima.sim(model=list(ar = 0.3), n = 10^4)
global_complexity(x = x, ndemb = 6)
# or:
opd = ordinal_pattern_distribution(x = x, ndemb = 6)
global_complexity(opd = opd, ndemb = 6)

References

Bandt, C. and Pompe, B., 2002. Permutation entropy: a natural complexity measure for time series. Physical review letters, 88(17), p.174102. Martin, M.T., Plastino, A. and Rosso, O.A., 2006. Generalized statistical complexity measures: Geometrical and analytical properties. Physica A: Statistical Mechanics and its Applications, 369(2), pp.439-462. Amigo, J., 2010. Permutation complexity in dynamical systems: ordinal patterns, permutation entropy and all that. Springer Science & Business Media.

Author(s)

Sebastian Sippel