| Box.test {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 |
type |
test to be performed: partial matching is used. |
fitdf |
number of degrees of freedom to be subtracted if |
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 (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. |
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. doi:10.2307/2284333.
Ljung, G. M. and Box, G. E. P. (1978), On a measure of lack of fit in time series models. Biometrika, 65, 297–303. doi:10.2307/2335207.
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")