Box.test {ts}R Documentation

Box-Pierce and Ljung-Box Tests


Compute the Box–Pierce or Ljung–Box test statistic for examining the null hypothesis of independence in a given time series.


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


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.


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. a character string giving the name of the data.


Missing values are not handled.


A. Trapletti


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.


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

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