# bds.test: BDS Test In tseries: Time Series Analysis and Computational Finance

 bds.test 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.out = 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
```

tseries documentation built on Oct. 10, 2022, 5:06 p.m.