nonlinearTseries (version 0.3.1)

mutualInformation: Average Mutual Information (AMI)

Description

Functions for estimating the Average Mutual Information (AMI) of a time series.

Usage

mutualInformation(
  time.series,
  lag.max = NULL,
  n.partitions = NULL,
  units = c("Nats", "Bits", "Bans"),
  do.plot = TRUE,
  ...
)
# S3 method for mutualInf
plot(
  x,
  main = "Average Mutual Information (AMI)",
  xlab = "Time lag",
  ylab = NULL,
  type = "h",
  ...
)
# S3 method for mutualInf
as.numeric(x, ...)
# S3 method for mutualInf
[(x, i)
# S3 method for mutualInf
[[(x, i)

Value

A mutualInf object that consist of a list containing all the relevant information of the AMI computation: time.lag, mutual.information, units and n.partitions.

Arguments

time.series

The observed time series.

lag.max

Largest lag at which to calculate the AMI.

n.partitions

Number of bins used to compute the probability distribution of the time series.

units

The units for the mutual information. Allowed units are "Nats", "Bits" or "Bans" (somethings called Hartleys). Default is "Nats".

do.plot

Logical value. If TRUE, the AMI is plotted

...

Further arguments for the plotting function.

x

A mutualInf object.

main

Title for the plot.

xlab

Title for the x axis.

ylab

Title for the y axis.

type

Type of plot to be drawn.

i

Indices specifying elements to extract.

Author

Constantino A. Garcia

Details

The Average Mutual Information (AMI) measures how much one random variable tells us about another. In the context of time series analysis, AMI helps to quantify the amount of knowledge gained about the value of \(x(t+\tau)\) when observing \(x(t)\).

To measure the AMI iof a time series, we create a histogram of the data using bins. Let \(p_i\) the probability that the signal has a value inside the ith bin, and let \(p_{ij}(\tau)\) be the probability that \(x(t)\) is in bin i ans \(x(t+\tau)\) is in bin j. Then, AMI for time delay \(\tau\) is defined as

$$AMI(\tau) = \sum_{i,j} p_{ij} log(\frac{p_{ij}}{p_i p_j})$$

Depending on the base of the logarithm used to define AMI, the AMI is measured in bits (base 2, also called shannons), nats (base e) or bans (base 10, also called hartleys).

References

H. Kantz and T. Schreiber: Nonlinear Time series Analysis (Cambridge university press) H. Abarbanel: Analysis of observed chaotic data (Springer, 1996).

See Also

timeLag

Examples

if (FALSE) {
sx = sinaiMap(a=0.3,n.sample=5000,start=c(0.23489,0.8923),do.plot=FALSE)$x
mutinf = mutualInformation(sx, n.partitions = 20, units = "Bits") }