# bartlettB.test: Bartlett's B test for white noise In hwwntest: Tests of White Noise using Wavelets

## Description

Bartlett's test uses the Kolmogorov-Smirnov test applied to the cumulative normalized periodogram.

## Usage

 `1` ```bartlettB.test(x, plot.it = FALSE) ```

## Arguments

 `x` The time series you wish to test, of any length. `plot.it` If TRUE then the normalized cumulative periodogram is plotted along with a straight line that indicates the theoretical line of this object under the null hypothesis. A further plot of the density of the true statistic under the null hypothesis is produced.

## Details

This test: (i) computes the periodogram, (ii) derives the normalized cumulative periodogram using the `cumperiod` function. Under the null hypothesis of white noise the periodogram is a set of iid exponential random variables, asymptotically. So, the cumulative periodogram should look like a straight line at a 45 degree angle. The test statistic is the maximum deviation of the normalized cumulative periodogram and this straight line. The p-value of the test is computed within the function by the `b.power` function. This is an example of a Kolmogorov-Smirnov statistical test.

## Value

An object of class `htest`. A list containing the following components:

 `statistic` The value of the Bartlett test statistic. `p.value` The p-value of the test `method` A text string saying what the method was

## Note

Code was based on Professor Newton's explanation

G. P. Nason

## References

Bartlett, M.S. (1967) Some Remarks on the Analysis of Time-Series. J. R. Statist. Soc. B, 54, 25-38.

http://www.stat.tamu.edu/~jnewton/stat626/topics/topics/topic13.pdf Link to Professor H. Joseph Newton's web page on Bartlett's test

Nason, G.P. and Savchev, D. (2014) White noise testing using wavelets. Stat, 3, 351-362. http://dx.doi.org/10.1002/sta4.69

`compute.rejection`, `cumperiod`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```# # Do white noise test on smallish data set # x <- rnorm(30) bartlettB.test(x) # # For my realization the answer was: # # # Bartlett B Test for white noise # #data: #= 0.3747, p-value = 0.999 # # So, we accept H_0 ```

### Example output

```	Bartlett B Test for white noise

data:
= 0.51667, p-value = 0.9523
```

hwwntest documentation built on May 29, 2017, 7:22 p.m.