Description Usage Arguments Details Value Note Author(s) References See Also Examples

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

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

`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. |

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.

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 |

Code was based on Professor Newton's explanation

G. P. Nason

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

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
``` |

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