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

transfer_entropy function