Box.test
BoxPierce and LjungBox Tests
Compute the BoxPierce or LjungBox test statistic for examining the null hypothesis of independence in a given time series. These are sometimes known as ‘portmanteau’ tests.
 Keywords
 ts
Usage
Box.test(x, lag = 1, type = c("BoxPierce", "LjungBox"), 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 nullhypothesis distribution is obtained by
setting fitdf = p+q
, provided of course that lag > fitdf
.
Value

A list with class
 statistic
 the value of the test statistic.
 parameter
 the degrees of freedom of the approximate chisquared
distribution of the test statistic (taking
fitdf
into account.  p.value
 the pvalue 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.
"htest"
containing the following components:
Note
Missing values are not handled.
References
Box, G. E. P. and Pierce, D. A. (1970), Distribution of residual correlations in autoregressiveintegrated moving average time series models. Journal of the American Statistical Association, 65, 15091526.
Ljung, G. M. and Box, G. E. P. (1978), On a measure of lack of fit in time series models. Biometrika 65, 297303.
Harvey, A. C. (1993) Time Series Models. 2nd Edition, Harvester Wheatsheaf, NY, pp.\ifelse{latex}{\out{~}}{ } 44, 45.
Examples
library(stats)
x < rnorm (100)
Box.test (x, lag = 1)
Box.test (x, lag = 1, type = "Ljung")