| 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 GEP, Pierce DA (1970). “Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models.” Journal of the American Statistical Association, 65(332), 1509–1526. doi:10.1080/01621459.1970.10481180.
Harvey AC (1993). Time Series Models, Second edition. Harvester Wheatsheaf. Pages 44–45.
Ljung GM, Box GEP (1978). “On a Measure of Lack of Fit in Time Series Models.” Biometrika, 65(2), 297–303. doi:10.1093/biomet/65.2.297.
Examples
x <- rnorm (100)
Box.test (x, lag = 1)
Box.test (x, lag = 1, type = "Ljung")