Box.test {stats} | R Documentation

## Box-Pierce and Ljung-Box Tests

### 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`.

### Value

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.

### Note

Missing values are not handled.

### Author(s)

A. Trapletti

### 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.

### Examples

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

[Package stats version 2.15.1 Index]