Cross-mapping from one variable to another variable over a range of lags. Wrapper around OnewayLaggedCCM allowing multiple values for each input argument. Useful when performing sensitivity tests. NOTE: automated optimisation of embedding parameters is only available in this function; lower-level functions do not implement them.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
ccm_lagged(data, lags = 0, Es = NULL, taus = NULL,
library.sizes = c(as.integer(nrow(data)/2)), lib = c(1, dim(data)[1]),
pred = lib, samples.original = 100, samples.surrogates = 50,
n.surrogates = 0, surrogate.methods = c("aaft"), time.unit = NULL,
time.bin.size = NULL, num.neighbours = NULL, random.libs = TRUE,
with.replacement = TRUE, exclusion.radius = NULL, epsilon = NULL,
RNGseed = 1111, silent = TRUE, time.run = F, print.to.console = T,
time.series.length.threshold = 100, library.column = 1,
target.column = 2, surrogate.column = target.column,
convergence.test = TRUE, parallel = TRUE, parallelize.on.each.lag = F,
num.cores = parallel::detectCores() - 1, regression.convergence.plots = F,
always.run.surrogates = F, n.libsizes.to.check = 20,
optimise.FNNdim = T, optimise.boxcountdim = T,
which.optimdim.test = "all", min.E = 2, max.E = 10, max.tau = 10,
plot.simplex.projection = F, ...)
``` |

`data` |
A data frame containing two columns - one for the presumed driver and one for the response. |

`lags` |
A vector of lags to compute CCM for. |

`Es` |
Vector of embedding dimensions. Defaults to NULL, which triggers automated optimisation of the embedding dimension up to the dimension specified by 'max.E'. |

`taus` |
Embedding lags. Can either be several types: 1. A vector of integer lags, in which case every lag provided is considered 2. NULL, which sets the embedding lag to a default value of 1. 3. "mi", which triggers automated optimisation of the embedding lag up to the dimension specified by 'max.tau' using the first minima of the lagged mutual information function. 4. "acf", which triggers automated optimisation of the embedding lag up to the dimension specified by 'max.tau' using the first minima of the lagged autocorrelation function. For densely sampled time series, the embedding lag should be set to the first minima of the autocorrelation ("acf"), or mutual information ("mi") functions. For sparsely sampled time series (for example geological time series), set the embedding lag(s) to low values (defaults to 1 if NULL). |

`library.sizes` |
The size of the random libraries drawn when calculating cross map skill. |

`lib` |
Indices of the original library time series to use as the library (training) set. |

`pred` |
Indices of the original target time series to use as prediction set. If this overlaps with the training set, make sure to use leave-K-out cross validation setting the 'exclusion.radius' parameters to a minimum of E + 1. |

`samples.original` |
The number of random libraries to draw when calculating cross map skill. |

`samples.surrogates` |
The number of surrogate series in each null ensemble. |

`n.surrogates` |
Should a surrogate test also be performed? If so, 'n.surrogates' sets the number of surrogate time series to use. By default, no surrogate test is performed (n.surrogates = 0). |

`surrogate.methods` |
Vector of types of surrogate time series to generate. Will vary depending on what null hypothesis is being tested. Defaults to AAFT surrogates. |

`time.unit` |
The time unit of the raw time series. |

`time.bin.size` |
The temporal resolution of the raw time series (given in the units indicated by 'time.unit'). |

`num.neighbours` |
The number of nearest neighbours to use in predictions. Defaults to NULL, in which case it is set to E + 1 for each analysis (this number will vary depending on the particular set of embedding parameters used for that analysis). |

`random.libs` |
Whether or not to sample random library (training) sets. Defaults to TRUE. |

`with.replacement` |
Should samples be drawn with replacement? Defaults to TRUE. |

`exclusion.radius` |
The number of temporal neighbours to exclude for the leave-K-out cross validation. Must be at least E + 1. Can be one of the following: 1. An integer, in which case that exclusion radius is used. 2. NULL, which sets the exclusion radius of E + 1. 3. "mi", which triggers automated optimisation of the exclusion radius up to using the first minima of the lagged mutual information function ran over a maximum lag approximately equal to 5 3. "acf", which triggers automated optimisation of the exclusion radius up to using the first minima of the lagged autocorrelation information function ran over a maximum lag approximately equal to 5 series length. If the embedding lag is high, the exclusion radius can be set to E + 1. If the embedding lag is low, the exclusion radius should be higher, or, even better, estimated using either "mi" or "acf". |

`epsilon` |
Exlude neighbours if the are within a distance of 'epsilon' from the predictee. |

`RNGseed` |
For reproducivility. Seed to use for the random number generator. |

`silent` |
Suppress warnings? |

`time.run` |
Time the run? |

`print.to.console` |
Display progress? |

`time.series.length.threshold` |
Display a warning if the time series length drops below this threshold. |

`library.column` |
Integer indicating which column to use as the library column (presumed response) (1 for the first column and 2 for the second column). |

`target.column` |
Integer indicating which column to use as the target column (presumed driver). Defaults to the opposite of 'library.column'. |

`surrogate.column` |
Which column to use to generate surrogates. Defaults to the value of 'target.column' (the presumed driver). |

`convergence.test` |
Should a convergence test be performed? Analyses where CCM does not convergence are nonsensical, so this option defaults to TRUE. |

`parallel` |
Activate parallellisation? Defaults to true. Currently, this only works decently on Mac and Linux systems. |

`parallelize.on.each.lag` |
Should parallellisation be done on the outer lag loop? Defaults to TRUE. Otherwise, parallellisation is done over the surrogate analyses. |

`num.cores` |
The number of CPU cores to use for parallelisation. Defaults to one core less than what is available. |

`regression.convergence.plots` |
Display regression plots for the convergence test? Defaults to FALSE. |

`always.run.surrogates` |
Should surrogate analyses be performed even if the convergence test fails? Defaults to FALSE (there is, usually, no reason to perform significance testing if the analysis is not causal to begin with). |

`n.libsizes.to.check` |
How many library sizes to use for the convergence check? Defaults to 30. |

`optimise.FNNdim` |
Optimise false nearest neighbours? Defaults to FALSE, meaning that simplex projection only is used for optimisation. If TRUE, simplex projection is performed with the minimum embedding dimension outputted from the FNN algorithm (and the box counting dimension, if acitivated). Only relevant if either 'E' or tau is set to NULL. |

`optimise.boxcountdim` |
Optimise box counting dimension? Defaults to FALSE, meaning that simplex projection only is used for optimisation. If TRUE, simplex projection is performed with the minimum embedding dimension as the first integer larger than twice the box counting algorithm of the attractor (also considering the minimum dimension indicated by the FNN algorithm, if activated). Only relevant if either 'E' or tau is set to NULL. |

`which.optimdim.test` |
Use the embedding dimension estimated by which optimisation procedure? Defaults to "all", which uses the maximum of the three methods. Other options are "FNN", "boxcount" or "simplex". |

`min.E` |
The minimum embedding dimension for which to optimise 'E'. Only relevant if 'Es' is set to NULL. |

`max.E` |
The maximum embedding dimension for which to optimise 'E'. Only relevant if 'Es' is set to NULL. |

`max.tau` |
The maximum embedding lag for which to optimise 'tau'. Only relevant if 'taus' is set to "mi" or "acf". |

`plot.simplex.projection` |
Plot simplex projection output? |

`...` |
Additional arguments to pass to lower-level functions. |

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