Box.test {ts} | 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.

### Usage

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

### 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. |

### 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. |

`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**, 553–564.

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")