Calculate Pattern Causality Using Lightweight Algorithm

Implements a computationally efficient version of the Pattern Causality Model Mk. II for analyzing causal interactions between two time series. This function uses pattern and signature spaces to assess causality through reconstructed state spaces and hashed pattern analysis.

Usage

pcLightweight(
  X,
  Y,
  E,
  tau,
  h,
  weighted,
  metric = "euclidean",
  distance_fn = NULL,
  state_space_fn = NULL,
  verbose = FALSE
)

Arguments

X

A numeric vector representing the first time series

Y

A numeric vector representing the second time series

E

Integer; embedding dimension for state space reconstruction (E > 1)

tau

Integer; time delay for state space reconstruction (tau > 0)

h

Integer; prediction horizon for future projections (h >= 0)

weighted

Logical; whether to use weighted causality strength calculations

metric

Character string specifying the distance metric; one of "euclidean", "manhattan", or "maximum"

distance_fn

Custom distance function for state space reconstruction

state_space_fn

Custom function for state space transformation

verbose

Logical; whether to display progress information (default: FALSE)

Value

An object of class "pc_fit" containing:

• total: Total causality strength (0-1)

• positive: Proportion of positive causality (0-1)

• negative: Proportion of negative causality (0-1)

• dark: Proportion of dark causality (0-1)

Details

Calculate Pattern Causality Using Lightweight Algorithm

The function implements these key steps:

• State space reconstruction using embedding parameters

• Pattern and signature space transformation

• Nearest neighbor analysis in reconstructed spaces

• Causality strength calculation using prediction accuracy

• Classification of causality types (positive/negative/dark)

See also

pcFullDetails for detailed analysis pcMatrix for analyzing multiple time series

Examples

data(climate_indices)
X <- climate_indices$AO
Y <- climate_indices$AAO
result <- pcLightweight(X, Y, E = 3, tau = 1, 
                       metric = "euclidean", h = 2, 
                       weighted = TRUE, verbose = FALSE)
print(result)
#> Pattern Causality Analysis Results:
#> Total: 0.3010
#> Positive: 0.2205
#> Negative: 0.3951
#> Dark: 0.3844
summary(result)
#> Pattern Causality Summary:
#> 
#> Causality Strengths:
#>       Type     Value
#> 1    Total 0.3009709
#> 2 Positive 0.2204697
#> 3 Negative 0.3951284
#> 4     Dark 0.3844019
plot(result)