Search for Optimal Parameters in Pattern Causality Analysis

Searches for the optimal embedding dimension (E) and time delay (tau) to maximize the accuracy of causality predictions in a dataset. This function implements a grid search approach to evaluate different parameter combinations.

Usage

optimalParametersSearch(
  Emax,
  tauMax,
  metric = "euclidean",
  distance_fn = NULL,
  state_space_fn = NULL,
  dataset,
  h = 0,
  weighted = FALSE,
  verbose = FALSE
)

Arguments

Emax

Positive integer > 2; maximum embedding dimension to test

tauMax

Positive integer; maximum time delay to test

metric

Character string; distance metric for causality analysis ('euclidean', 'manhattan', 'maximum'). Defaults to "euclidean". Ignored if distance_fn is provided.

distance_fn

Optional custom distance function; takes two numeric vectors as input and returns a numeric distance. (default: NULL)

state_space_fn

Optional custom function for state space reconstruction; takes a numeric vector and parameters E and tau as input and returns a reconstructed state space. (default: NULL)

dataset

Numeric matrix; each column represents a time series.

h

Positive integer; prediction horizon.

weighted

Logical; if TRUE, weighted causality analysis is performed.

verbose

Logical; if TRUE, prints progress information. (default: FALSE)

Value

A pc_params object containing:

• accuracy_summary: A data frame summarizing the accuracy for each parameter combination.

• computation_time: The time taken for the analysis.

• parameters: A list of the input parameters used.

Details

Search for Optimal Parameters in Pattern Causality Analysis

This function evaluates each combination of embedding dimension and time delay for their effectiveness in detecting different types of causality:

• Total causality: Overall causal relationship strength

• Positive causality: Direct positive influences

• Negative causality: Direct negative influences

• Dark causality: Complex or indirect causal relationships

Examples

# \donttest{
data(climate_indices)
dataset <- climate_indices[, -1]
optimalParams <- optimalParametersSearch(
  Emax = 3, 
  tauMax = 3, 
  metric = "euclidean",
  dataset = dataset,
  h = 1,
  weighted = FALSE
)
print(optimalParams)
#> Pattern Causality Parameter Optimization Results
#> ---------------------------------------------
#> Computation time: 14.39181 secs 
#> 
#> Parameters tested:
#>   Emax: 3 
#>   tauMax: 3 
#>   Metric: euclidean 
#> 
#> First few values:
#>         E tau     Total  Positive  Negative         Dark
#> Combo 1 2   1 0.5006373 0.4970317 0.5022991 0.0006691879
#> Combo 2 2   2 0.5009615 0.5015466 0.4962184 0.0022350584
#> Combo 3 2   3 0.5130561 0.5279035 0.4708467 0.0012498304
#> Combo 4 3   1 0.2824968 0.2719238 0.2576842 0.4703920280
#> Combo 5 3   2 0.2796224 0.2870213 0.2875241 0.4254546326
#> Combo 6 3   3 0.2944664 0.3240271 0.2823818 0.3935910495
#> 
# }