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.
Box.test(x, lag = 1, type = c("Box-Pierce", "Ljung-Box"), fitdf = 0)a numeric vector or univariate time series.
the statistic will be based on lag autocorrelation
coefficients.
test to be performed: partial matching is used.
number of degrees of freedom to be subtracted if x
is a series of residuals.
A list with class "htest" containing the following components:
the value of the test statistic.
the degrees of freedom of the approximate chi-squared
distribution of the test statistic (taking fitdf into account.
the p-value of the test.
a character string indicating which type of test was performed.
a character string giving the name of the data.
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.
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, 297--303.
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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