# Box.test {stats}

### Description

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.

### 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`

.

### Values

A list with class `"htest"`

containing the following components:

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

into account. - p.value
- the p-value of the test.
- method
- a character string indicating which type of test was performed.
- data.name
- a character string giving the name of the data.

### 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.

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

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

### Note

Missing values are not handled.

Documentation reproduced from R 3.0.2. License: GPL-2.