# bds.test

From tseries v0.9-20
by Kurt Hornik

##### BDS Test

Computes and prints the BDS test statistic for the null that `x`

is a series of i.i.d. random variables.

- Keywords
- ts

##### 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.

##### 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
```

*Documentation reproduced from package tseries, version 0.9-20, License: GPL (see file COPYING)*

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