tseries (version 0.7-4)

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 = 2, eps = seq(0.5*sd(x),2*sd(x),length=4), trace =
          FALSE)
print (object, digits = 4)

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.

object

a list with class "bdstest".

digits

the number of digits to format real numbers.

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.

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.

References

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

Examples

x <- rnorm (100)
bds.test (x, m = 3)  # i.i.d. example

x <- c (rnorm(50), runif(50))
bds.test (x, m = 3)  # not identically distributed

x <- quadmap (xi = 0.2, a = 4.0, n = 100)
bds.test (x, m = 3)  # not independent