# Description: Surrogates Early Warning Signals

### Description

`surrogates_ews`

is used to estimate distributions
of trends in statistical moments from different surrogate
timeseries generated after fitting an ARMA(p,q) model on
the data. The trends are estimated by the nonparametric
Kendall tau correlation coefficient and can be compared
to the trends estimated in the original timeseries to
produce probabilities of false positives.

### Usage

1 2 3 4 5 6 |

### Arguments

`timeseries` |
a numeric vector of the observed univariate timeseries values or a numeric matrix where the first column represents the time index and the second the observed timeseries values. Use vectors/matrices with headings. |

`indicator` |
is the statistic (leading indicator)
selected for which the surrogate timeseries are produced.
Currently, the indicators supported are: |

`winsize` |
is the size of the rolling window expressed as percentage of the timeseries length (must be numeric between 0 and 100). Default valuise 50%. |

`detrending` |
the timeseries can be
detrended/filtered prior to analysis. There are three
options: |

`bandwidth` |
is the bandwidth used for the Gaussian
kernel when gaussian filtering is selected. It is
expressed as percentage of the timeseries length (must be
numeric between 0 and 100). Alternatively it can be given
by the bandwidth selector |

`boots` |
the number of surrogate data. Default is 100. |

`logtransform` |
logical. If TRUE data are logtransformed prior to analysis as log(X+1). Default is FALSE. |

`interpolate` |
logical. If TRUE linear interpolation is applied to produce a timeseries of equal length as the original. Default is FALSE (assumes there are no gaps in the timeseries). |

### Details

see ref below

### Value

`surrogates_ews`

returns a matrix that contains:

`Kendall tau estimate original` |
the trends of the original timeseries. |

`Kendall tau p-value original` |
the p-values of the trends of the original timeseries. |

`Kendall tau estimate surrogates` |
the trends of the surrogate timeseries. |

`Kendall tau p-value surrogates` |
the associated p-values of the trends of the surrogate timeseries. |

`significance p` |
the p-value for the original Kendall tau rank correlation estimate compared to the surrogates. |

In addition, `surrogates_ews`

returns a plot with
the distribution of the surrogate Kendall tau estimates
and the Kendall tau estimate of the original series.
Vertical lines indicate the 5% and 95% significance
levels.

### Author(s)

Vasilis Dakos vasilis.dakos@gmail.com

### References

Dakos, V., et al (2008). "Slowing down as an early
warning signal for abrupt climate change."
*Proceedings of the National Academy of Sciences*
105(38): 14308-14312

Dakos, V., et al (2012)."Methods for Detecting Early
Warnings of Critical Transitions in Time Series
Illustrated Using Simulated Ecological Data." *PLoS
ONE* 7(7): e41010. doi:10.1371/journal.pone.0041010

### See Also

`generic_ews`

; `ddjnonparam_ews`

;
`bdstest_ews`

; `sensitivity_ews`

;
`surrogates_ews`

; `ch_ews`

;
`movpotential_ews`

;
`livpotential_ews`

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