tseries (version 0.10-58)

bds.test: BDS Test

Description

Computes and prints the BDS test statistic for the null that x is a series of i.i.d. random variables.

Usage

bds.test(x, m = 3, eps = seq(0.5 * sd(x), 2 * sd(x), length.out = 4),
         trace = FALSE)

Value

A list with class "bdstest" containing the following components:

statistic

the values of the test statistic.

p.value

the p-values of the test.

method

a character string indicating what type of test was performed.

parameter

a list with the components m and eps containing the embedding dimensions and epsilon values for which the statistic is computed.

data.name

a character string giving the name of the data.

Arguments

x

a numeric vector or time series.

m

an integer indicating that the BDS test statistic is computed for embedding dimensions 2, ..., m.

eps

a numeric vector of epsilon values for close points. The BDS test is computed for each element of eps. It should be set in terms of the standard deviation of x.

trace

a logical indicating whether some informational output is traced.

Author

B. LeBaron, Ported to R by A. Trapletti

Details

This test examines the ``spatial dependence'' of the observed series. To do this, the series is embedded in m-space and the dependence of x is examined by counting ``near'' points. Points for which the distance is less than eps are called ``near''. The BDS test statistic is asymptotically standard Normal.

Missing values are not allowed.

There is a special print method for objects of class "bdstest" which by default uses 4 digits to format real numbers.

References

J. B. Cromwell, W. C. Labys and M. Terraza (1994): Univariate Tests for Time Series Models, Sage, Thousand Oaks, CA, pages 32--36.

Examples

x <- rnorm(100)
bds.test(x)  # i.i.d. example

x <- c(rnorm(50), runif(50))
bds.test(x)  # not identically distributed

x <- quadmap(xi = 0.2, a = 4.0, n = 100)
bds.test(x)  # not independent