Box.test {stats} | R Documentation |

## \IBox-\IPierce and \ILjung-\IBox Tests

### Description

Compute the \IBox–\IPierce or \ILjung–\IBox 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 |

`type` |
test to be performed: partial matching is used. |

`fitdf` |
number of degrees of freedom to be subtracted if |

### 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 |

`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.
doi: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.
doi:10.2307/2335207.

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")
```

*stats*version 4.4.0 Index]