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. These are
sometimes known as
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
- test to be performed: partial matching is used.
- number of degrees of freedom to be subtracted if
xis a series of residuals.
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
fitdf = p+q, provided of course that
lag > fitdf.
- 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
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.
Missing values are not handled.
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.
x <- rnorm (100) Box.test (x, lag = 1) Box.test (x, lag = 1, type = "Ljung")