# bds.test

From tseries v0.7-4
by Adrian Trapletti

##### 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 = 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.

##### 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.

##### 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, 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
```

*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.*

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