Generate directed coupling signals

Creates a pair of signals where x drives y with a specified lag and coupling strength. Signal x is white noise, and y is a mixture of a lagged copy of x and independent noise. This is useful for testing directed coupling measures such as Granger causality.

Usage

make_directed_signals(n = 5000, sr = 500, lag_samples = 10, coupling = 0.7)

Arguments

n

Integer number of samples (default 5000).

sr

Numeric sampling rate in Hz (default 500).

lag_samples

Integer number of samples by which x leads y (default 10).

coupling

Numeric coupling strength in [0, 1] (default 0.7).

Value

A named list with components:

x

Numeric vector – driving signal (white noise).

y

Numeric vector – driven signal (lagged mixture).

sr

Numeric sampling rate.

lag_samples

Integer lag used.

Details

The generating model is: $$y(t) = \text{coupling} \cdot x(t - \text{lag\_samples}) + (1 - \text{coupling}) \cdot \epsilon(t)$$ where \(\epsilon(t) \sim N(0, 1)\).

References

Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424–438.

See also

grangerCausality(), make_coupled_signals(), crossCorrelation(), couplingAnalysis()

Examples

signals <- make_directed_signals(n = 5000, sr = 500,
                                  lag_samples = 10, coupling = 0.7)
result <- grangerCausality(signals$x, signals$y, sr = signals$sr,
                           order = 15)
result$gc_xy   # should be positive (x drives y)
#> [1] 1.846288
result$net_gc  # should be positive
#> [1] 1.843261