Simulate a pair of multivariate series with a known lag — simulate_lagged

Generates X as a multivariate seasonal series (sinusoids with a random common phase and staggered offsets among variables) plus AR(1) noise. Under the null (true_lag = NULL), Y is an independent draw from the same generator. Otherwise Y at time t is a linear map of X at time t - true_lag plus AR(1) noise; X is generated over n_times + true_lag points so that every row of Y has a source in X.

Usage

simulate_lagged_series(
  n_times = 24,
  n_vars_x = 5,
  n_vars_y = 5,
  true_lag = NULL,
  period = 12,
  amplitude = 1,
  autocorr = 0.5,
  noise_sd = 1,
  seed = NULL
)

Arguments

n_times: Number of time points.
n_vars_x, n_vars_y: Number of variables in X and Y.
true_lag: NULL for independent series, or a non-negative integer lag by which X leads Y. 0 means a contemporaneous association, not the absence of one.
period: Length of the seasonal cycle, in time steps.
amplitude: Amplitude of the seasonal sinusoids.
autocorr: AR(1) coefficient of the noise, in (-1, 1).
noise_sd: Marginal standard deviation of the AR(1) noise.
seed: Optional integer seed. The global random number stream is left untouched.

Value

A list with matrices X (n_times x n_vars_x) and Y (n_times x n_vars_y), and true_lag.

Details

Setting amplitude = 0 removes the seasonal component and leaves pure AR(1) series; setting autocorr = 0 gives white noise around the seasonal signal (the design of the original simulation, Appendix S1).

Examples

null_pair <- simulate_lagged_series(n_times = 12, seed = 42)
lagged_pair <- simulate_lagged_series(n_times = 24, true_lag = 3, seed = 42)
str(lagged_pair)
#> List of 3
#>  $ X       : num [1:24, 1:5] 1.61 1.037 0.251 1.715 -0.572 ...
#>  $ Y       : num [1:24, 1:5] 2.309 0.727 0.574 1.5 2.748 ...
#>  $ true_lag: num 3