# Box.test {stats}

Box-Pierce and Ljung-Box Tests
Package:
stats
Version:
R 3.0.2

### 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.

### Examples

```x <- rnorm (100)
Box.test (x, lag = 1)
Box.test (x, lag = 1, type = "Ljung")```

### Author(s)

A. Trapletti

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