transfer_entropy function

Function to estimate Shannon and Renyi transfer entropy between two time series x and y.

transfer_entropy(
  x,
  y,
  lx = 1,
  ly = 1,
  q = 0.1,
  entropy = "Shannon",
  shuffles = 100,
  type = "quantiles",
  quantiles = c(5, 95),
  bins = NULL,
  limits = NULL,
  nboot = 300,
  burn = 50,
  quiet = NULL,
  seed = NULL,
  na.rm = TRUE
)

Arguments

• x: a vector of numeric values, ordered by time. Also allowed are xts, zoo, or ts objects.
• y: a vector of numeric values, ordered by time. Also allowed are xts, zoo, or ts objects.
• lx: Markov order of x, i.e. the number of lagged values affecting the current value of x. Default is lx = 1.
• ly: Markov order of y, i.e. the number of lagged values affecting the current value of y. Default is ly = 1.
• q: a weighting parameter used to estimate Renyi transfer entropy, parameter is between 0 and 1. For q = 1, Renyi transfer entropy converges to Shannon transfer entropy. Default is q = 0.1.
• entropy: specifies the transfer entropy measure that is estimated, either 'Shannon' or 'Renyi'. The first character can be used to specify the type of transfer entropy as well. Default is entropy = 'Shannon'.
• shuffles: the number of shuffles used to calculate the effective transfer entropy. Default is shuffles = 100.
• type: specifies the type of discretization applied to the observed time series:'quantiles', 'bins' or 'limits'. Default is type = 'quantiles'.
• quantiles: specifies the quantiles of the empirical distribution of the respective time series used for discretization. Default is quantiles = c(5,95).
• bins: specifies the number of bins with equal width used for discretization. Default is bins = NULL.
• limits: specifies the limits on values used for discretization. Default is limits = NULL.
• nboot: the number of bootstrap replications for each direction of the estimated transfer entropy. Default is nboot = 300.
• burn: the number of observations that are dropped from the beginning of the bootstrapped Markov chain. Default is burn = 50.
• quiet: if FALSE (default), the function gives feedback.
• seed: a seed that seeds the PRNG (will internally just call set.seed), default is seed = NULL.
• na.rm: if missing values should be removed (will remove the values at the same point in the other series as well). Default is TRUE.

Returns

an object of class transfer_entropy, containing the transfer entropy estimates in both directions, the effective transfer entropy estimates in both directions, standard errors and p-values based on bootstrap replications of the Markov chains under the null hypothesis of statistical independence, an indication of statistical significance, and quantiles of the bootstrap samples (if nboot > 0).

Examples

# construct two time-series
set.seed(1234567890)
n <- 500
x <- rep(0, n + 1)
y <- rep(0, n + 1)

for (i in seq(n)) {
  x[i + 1] <- 0.2 * x[i] + rnorm(1, 0, 2)
  y[i + 1] <- x[i] + rnorm(1, 0, 2)
}

x <- x[-1]
y <- y[-1]

# Calculate Shannon's Transfer Entropy
te_result <- transfer_entropy(x, y, nboot = 100)
te_result

summary(te_result)

  # Parallel Processing using the future-package
  library(future)
  plan(multisession)

  te_result2 <- transfer_entropy(x, y, nboot = 100)
  te_result2

  # revert back to sequential execution
  plan(sequential)

  te_result2 <- transfer_entropy(x, y, nboot = 100)
  te_result2

  # General set of quiet
  set_quiet(TRUE)
  a <- transfer_entropy(x, y, nboot = 0)

  set_quiet(FALSE)
  a <- transfer_entropy(x, y, nboot = 0)

  # close multisession, see also ?plan
  plan(sequential)

See Also

coef, print.transfer_entropy