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.
ccm(block, lib = NULL, pred = NULL, norm = 2, E = 1, tau = -1,
tp = 0, num_neighbors = "e+1", lib_sizes = c(10, 75, 5),
random_libs = TRUE, num_samples = 100, replace = FALSE, lib_column = 1,
target_column = 2, first_column_time = FALSE, RNGseed = NULL,
exclusion_radius = NULL, epsilon = NULL, stats_only = TRUE,
silent = TRUE)If stats_only = TRUE: a data.frame with forecast statistics for both the forward and reverse mappings:
| LibSize | library length (number of vectors) |
| x:y | cross mapped correlation coefficient between observations x and predictions y |
| y:x | cross mapped correlation coefficient between observations y and predictions x |
| E | embedding dimension |
| tau | time delay offset |
| tp | forecast interval |
| nn | number nearest neighbors |
If stats_only = FALSE: a named list with the following items: settings:
| LibMeans | data.frame with the mean bidirectional forecast statistics |
| CCM1_PredictStat | data.frame with forward mapped prediction statistics for each prediction of the ensemble |
| CCM1_Predictions | list of prediction result data.frame each forward mapped prediction of the ensemble |
| CCM2_PredictStat | data.frame with reverse mapped prediction statistics for each prediction of the ensemble |
| CCM2_Predictions | list of prediction result data.frame each reverse mapped prediction of the ensemble |
CCM1_PredictStat and CCM2_PredictStat data.frames have columns:
| N | prediction number |
| E | embedding dimension |
| nn | number of nearest neighbors |
| tau | embedding time delay offset |
| LibSize | library size |
| rho | correlation coefficient |
| RMSE | root mean square error |
| MAE | maximum absolute error |
| lib | column name of the library vector |
| target | column name of the target vector |
either a vector to be used as the time series, or a data.frame or matrix where each column is a time series
a 2-column matrix, data.frame, 2-element vector or string of row indice pairs, where each pair specifies the first and last *rows* of the time series to create the library. If not specified, all available rows are used
(same format as lib), but specifying the sections of the time series to forecast. If not specified, set equal to lib
the distance measure to use. see 'Details'
the embedding dimensions to use for time delay embedding
the time-delay offset to use for time delay embedding
the prediction horizon (how far ahead to forecast)
the number of nearest neighbors to use. Note that the default value will change depending on the method selected. (any of "e+1", "E+1", "e + 1", "E + 1" will set this parameter to E+1 for each run
three integers specifying the start, stop and increment index of library sizes
indicates whether to use randomly sampled libs
is the number of random samples at each lib size (this parameter is ignored if random_libs is FALSE)
indicates whether to sample vectors with replacement
name (index) of the column to cross map from
name (index) of the column to forecast
indicates whether the first column of the given block is a time column
will set a seed for the random number generator, enabling reproducible runs of ccm with randomly generated libraries
excludes vectors from the search space of nearest neighbors if their *time index* is within exclusion_radius (NULL turns this option off)
not implemented
specify whether to output just the forecast statistics or the raw predictions for each run
prevents warning messages from being printed to the R console
ccm runs both forward and reverse cross maps in seperate
threads. Results are returned for both mappings.
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 75 in increments of
5.
norm = 2 (only option currently available) uses the "L2 norm",
Euclidean distance:
$$distance(a,b) := \sqrt{\sum_i{(a_i - b_i)^2}}
$$
anchovy_xmap_sst <- ccm(sardine_anchovy_sst, E = 3,
lib_column = "anchovy", target_column = "np_sst",
lib_sizes = c(10, 75, 5), num_samples = 100)
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