Box.test                package: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.

 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")

