# Box.test

##### Box-Pierce and Ljung-Box Tests

Compute the Box--Pierce or Ljung--Box test statistic for examining the null hypothesis of independence in a given time series. These are sometimes known as ‘portmanteau’ tests.

- Keywords
- ts

##### Usage

`Box.test(x, lag = 1, type = c("Box-Pierce", "Ljung-Box"), fitdf = 0)`

##### Arguments

- x
a numeric vector or univariate time series.

- lag
the statistic will be based on

`lag`

autocorrelation coefficients.- type
test to be performed: partial matching is used.

- fitdf
number of degrees of freedom to be subtracted if

`x`

is a series of residuals.

##### Details

These tests are sometimes applied to the residuals from an
`ARMA(p, q)`

fit, in which case the references suggest a better
approximation to the null-hypothesis distribution is obtained by
setting `fitdf = p+q`

, provided of course that `lag > fitdf`

.

##### Value

A list with class `"htest"`

containing the following components:

the value of the test statistic.

the degrees of freedom of the approximate chi-squared
distribution of the test statistic (taking `fitdf`

into account).

the p-value of the test.

a character string indicating which type of test was performed.

a character string giving the name of the data.

##### Note

Missing values are not handled.

##### References

Box, G. E. P. and Pierce, D. A. (1970),
Distribution of residual correlations in autoregressive-integrated
moving average time series models.
*Journal of the American Statistical Association*, **65**,
1509--1526.
10.2307/2284333.

Ljung, G. M. and Box, G. E. P. (1978),
On a measure of lack of fit in time series models.
*Biometrika*, **65**, 297--303.
10.2307/2335207.

Harvey, A. C. (1993)
*Time Series Models*.
2nd Edition, Harvester Wheatsheaf, NY, pp.44, 45.

##### Examples

`library(stats)`

```
# NOT RUN {
x <- rnorm (100)
Box.test (x, lag = 1)
Box.test (x, lag = 1, type = "Ljung")
# }
```

*Documentation reproduced from package stats, version 3.6.2, License: Part of R 3.6.2*