R: BDS Test

bds.test {tseries} | R Documentation

## 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 = 4),
             trace = FALSE)

### 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.

### 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.

### 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.

### Author(s)

B. LeBaron, Ported to R by A. Trapletti

### 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

[Package tseries version 0.10-47 Index]