# amif

0th

Percentile

##### Auto Mutual Information Function

Computes and plots the sample (normalized) auto mutual information function of x up to lag lag.max.

Keywords
ts
##### Usage
amif (x, lag.max = NULL, maxbit = 20, confidence = 0.2, ci = 0.95, nsurr = 20,
fft = FALSE, amplitude = FALSE, normalized = TRUE, trace = FALSE,
plot = TRUE, ...)
plot (object, ci.col = "blue", ylab = "AMIF", ...)
##### Arguments
x
a numeric vector or time series.
lag.max
a scalar lag parameter.
maxbit
the maximum resolution in bit to which the precision of the data will be limited; also limits the maximum partition depth. It cannot exceed an overall maximum of 25 bit.
confidence
the confidence level for the chi-square-test which tests the point distribution in substructures of the probability area upon uniformity. A substructure is assumed if the deviation from a uniform point distribution occurs with a probability
ci
coverage probability for confidence bound. Plotting of the confidence bound is suppressed if ci is zero or negative.
nsurr
the number of surrogate samples to compute the confidence bound. To obtain "good" confidence bounds, set nsurr to at least a value of 500.
fft
a logical indicating whether phase randomized surrogate data is generated.
amplitude
a logical indicating whether amplitude-adjusted surrogate data is computed.
normalized
a logical indicating whether the normalized auto mutual information function is computed.
trace
a logical indicating whether additional output from the computation is traced.
plot
a logical indicating whether the AMIF is plotted.
object
an object of class "amif".
ci.col
color to plot the confidence bound.
ylab
the title for the y axis.
...
either additional arguments to plot.amif (amif), or additional arguments to plot.acf (plot.amif).
##### Details

If plot is TRUE, then the AMIF is plotted. Further, the confidence bound for the null of surrogate data is computed by Monte-Carlo simulation percentiles and plotted. If any temporal dependence is under question, then the null is an i.i.d. series and scrambled surrogates can be used (the default). In the case of testing non-linearity against linearity, setting the switch fft is appropriate. It generates surrogates with the same spectrum as x. If the switch amplitude is set in addition, then surrogates xs with the following properties are used: First, xs has the same histogram as x. Second, G(xs) has the same Fourier spectra as G(x), where G(.) is the transformation from the histogram of x to a Gaussian distribution.

The simulations are computed with the actual values of maxbit and confidence.

Missing values are not allowed.

To compute the mutual information between two random variables, an implementation of the algorithm of Fraser and Swinney (1986) is used.

##### Value

• An object of class c("amif","acf").

##### References

C. Granger and J. L. Lin (1994): Using the Mutual Information Coefficient to Identify Lags in Non-Linear Models. Journal of Time Series Analysis 15, pp. 371-384.

A. M. Fraser and H. L. Swinney (1986): Independent Coordinates for Strange Attractors from Mutual Information. Physical Review A 33, pp. 1134-1140.

acf, surrogate

• amif
• plot.amif
##### Examples
n <- 1000  # Length of simulated time series

e <- rnorm (n)  # Generate ARCH(1) process
x <- double (n)
x <- rnorm (1)
for (i in 2:n)
{
x[i] <- e[i]*sqrt(0.1+0.4*x[i-1]^2)
}
x <- ts(x)
plot (x)

# Each test takes about 3 sec on a Pentium II 300MHz

amif (x, lag.max=5)  # i.i.d. vs. any dependence
amif (x, lag.max=5, fft=TRUE)  # linear vs. non-linear
amif (x, lag.max=5, fft=TRUE, amplitude=TRUE)

e <- rnorm (n)  # Generate AR(1) process
x <- double (n)
x <- rnorm (1)
for (i in 2:n)
{
x[i] <- 0.4*x[i-1]+e[i]
}
x <- ts(x)
plot (x)

amif (x, lag.max=5)  # i.i.d. vs. any dependence
amif (x, lag.max=5, fft=TRUE)  # linear vs. non-linear
amif (x, lag.max=5, fft=TRUE, amplitude=TRUE)
Documentation reproduced from package tseries, version 0.7-4, License: GPL (see file COPYING), except for ./src/muin2ser.f and ./misc which are free for non-commercial purposes. See file README for details.

### Community examples

Looks like there are no examples yet.