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.

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")


[Package stats version 4.3.0 Index]