In BZPaper/RTransferEntropy: Measuring Information Flow Between Time Series with Shannon and Renyi Transfer Entropy

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RTransferEntropy

The goal of RTransferEntropy is to implement the calculation of the transfer entropy metric using Shannon's or the Renyi's methodology.

A short introduction can be found below, for a more thorough introduction to the transfer entropy methodology and the RTransferEntropy package, see the vignette and the RTransferEntropy paper. If you use the package in academic work, please make sure to cite us, see also citation("RTransferEntropy").

The authors of the TransferEntropy package no longer develop their package, which is deprecated as of 2018-08-10, and recommend the use of this package.

Installation

You can install RTransferEntropy with

install.packages("RTransferEntropy")

or the development version from github with

# install.packages("devtools")
devtools::install_github("BZPaper/RTransferEntropy")

Example using simulated data

Simulate a simple model to obtain two time series that are not independent (see simulation study in Dimpfl and Peter (2013)), i.e. one time series is lag of the other plus noise. In this case, one expects significant information flow from x to y and none from y to x.

Simulating a Time-Series

library(RTransferEntropy)
library(future)
# enable parallel processing
plan(multisession)

set.seed(20180108)
n <- 2000
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]

Visualisation

library(ggplot2)
library(gridExtra)
theme_set(theme_light())

# Lagged X-Plot
p1 <- ggplot(data.frame(x = c(NA, x[1:(length(x) - 1)]), y = y), aes(x, y)) +
  geom_smooth() +
  geom_point(alpha = 0.5, size = 0.5) +
  labs(x = expression(X[t - 1]), y = expression(Y[t])) +
  coord_fixed(1) +
  scale_x_continuous(limits = range(x)) +
  scale_y_continuous(limits = range(y))

# X-Y Plot
p2 <- ggplot(data.frame(x = x, y = y), aes(x, y)) +
  geom_smooth() +
  geom_point(alpha = 0.5, size = 0.5) +
  labs(x = expression(X[t]), y = expression(Y[t])) +
  coord_fixed(1) +
  scale_x_continuous(limits = range(x)) +
  scale_y_continuous(limits = range(y))

# Lagged Y Plot
p3 <- ggplot(data.frame(x = x, y = c(NA, y[1:(length(y) - 1)])), aes(x, y)) +
  geom_smooth() +
  geom_point(alpha = 0.5, size = 0.5) +
  labs(x = expression(X[t]), y = expression(Y[t - 1])) +
  coord_fixed(1) +
  scale_x_continuous(limits = range(x)) +
  scale_y_continuous(limits = range(y))

a <- grid.arrange(p1, p2, p3, ncol = 3)

Shannon Transfer Entropy

set.seed(20180108 + 1)

shannon_te <- transfer_entropy(x = x, y = y)

shannon_te

summary(shannon_te)

Alternatively, you can calculate only the transfer entropy or the effective transfer entropy with

calc_te(x, y)
calc_te(y, x)

calc_ete(x, y)
calc_ete(y, x)

Renyi Transfer Entropy

set.seed(20180108 + 1)

renyi_te <- transfer_entropy(x = x, y = y, entropy = "renyi", q = 0.5)

renyi_te

calc_te(x, y, entropy = "renyi", q = 0.5)
calc_te(y, x, entropy = "renyi", q = 0.5)

calc_ete(x, y, entropy = "renyi", q = 0.5)
calc_ete(y, x, entropy = "renyi", q = 0.5)

Function Verbosity aka `quiet = TRUE`

To disable the verbosity of a function you can use the argument quiet. Note that we have set nboot = 0 as we don't need bootstrapped quantiles for this example.

te <- transfer_entropy(x, y, nboot = 0, quiet = T)

te

If you want to disable feedback from transfer_entropy functions, you can do so by using set_quiet(TRUE)

set_quiet(TRUE)
te <- transfer_entropy(x, y, nboot = 0)

te

# revert back with
set_quiet(FALSE)

te <- transfer_entropy(x, y, nboot = 0)

Parallel Programming

Using the future package and its plans we can execute all computations in parallel like so

library(future)
plan(multisession)
te <- transfer_entropy(x, y, nboot = 100)

# revert to sequential mode
plan(sequential)
te <- transfer_entropy(x, y, nboot = 100)

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