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

### Description

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

### Usage

1 | ```
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. |

### 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)

### Value

A named vector containing the three global complexity measures.

### Author(s)

Sebastian Sippel

### 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.

### Examples

1 2 3 4 5 | ```
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)
``` |