ccm {rEDM} | R Documentation

## Perform convergent cross mapping using simplex projection

### Description

`ccm` uses time delay embedding on one time series to generate an attractor reconstruction, and then applies the simplex projection algorithm to estimate concurrent values of another time series. This method is typically applied, varying the library sizes, to determine if one time series contains the necessary dynamic information to recover the influence of another, causal variable.

### Usage

    ccm(block, lib = c(1, NROW(block)), pred = lib,
      norm_type = c("L2 norm", "L1 norm", "LP norm"), P = 0.5, E = 1,
      tau = 1, tp = 0, num_neighbors = "e+1", lib_sizes = seq(10, 100,
      by = 10), random_libs = TRUE, num_samples = 100, replace = TRUE,
      lib_column = 1, target_column = 2, first_column_time = FALSE,
      RNGseed = NULL, exclusion_radius = NULL, epsilon = NULL,
      silent = FALSE)

### Arguments

`block` | either a vector to be used as the time series, or a data.frame or matrix where each column is a time series
`lib` | a 2-column matrix (or 2-element vector) where each row specifes the first and last *rows* of the time series to use for attractor reconstruction
`pred` | (same format as lib), but specifying the sections of the time series to forecast.
`norm_type` | the distance function to use. see 'Details'
`P` | the exponent for the P norm
`E` | the embedding dimensions to use for time delay embedding
`tau` | the lag to use for time delay embedding
`tp` | the prediction horizon (how far ahead to forecast)
`num_neighbors` | the number of nearest neighbors to use (any of "e+1", "E+1", "e + 1", "E + 1" will peg this parameter to E+1 for each run, any value < 1 will use all possible neighbors.)
`lib_sizes` | the vector of library sizes to try
`random_libs` | indicates whether to use randomly sampled libs
`num_samples` | is the number of random samples at each lib size (this parameter is ignored if random_libs is FALSE)
`replace` | indicates whether to sample vectors with replacement
`lib_column` | the index (or name) of the column to cross map from
`target_column` | the index (or name) of the column to cross map to
`first_column_time` | indicates whether the first column of the given block is a time column (and therefore excluded when indexing)
`RNGseed` | will set a seed for the random number generator, enabling reproducible runs of ccm with randomly generated libraries
`exclusion_radius` | excludes vectors from the search space of nearest neighbors if their *time index* is within exclusion_radius (NULL turns this option off)
`epsilon` | excludes vectors from the search space of nearest neighbors if their *distance* is farther away than epsilon (NULL turns this option off)
`silent` | prevents warning messages from being printed to the R console

### Details

The default parameters are set so that passing a matrix as the only argument will use E = 1 (embedding dimension), and leave-one-out cross-validation over the whole time series to compute cross-mapping from the first column to the second column, letting the library size vary from 10 to 100 in increments of 10.

norm_type "L2 norm" (default) uses the typical Euclidean distance:

distance(a, b) := √(∑(a_i - b_i)^2)

norm_type "L1 norm" uses the Manhattan distance:

distance(a, b) := ∑|a_i - b_i|

norm type "P norm" uses the LP norm, generalizing the L1 and L2 norm to use $p$ as the exponent:

distance(a, b) := (∑(a_i - b_i)^p)^(1/p)

### Value

A data.frame with forecast statistics for the different parameter settings:

L | library length (number of vectors)
num_pred | number of predictions
rho | correlation coefficient between observations and predictions
mae | mean absolute error
rmse | root mean square error

### Examples

    data("sardine_anchovy_sst")
    anchovy_xmap_sst <- ccm(sardine_anchovy_sst, E = 3,
      lib_column = "anchovy", target_column = "np_sst",
      lib_sizes = seq(10, 80, by = 10), num_samples = 100)

[Package rEDM version 0.7.2 Index]