Box.test
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 ‘portmanteau’ tests.
- Keywords
- ts
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
lagautocorrelation coefficients. - type
- test to be performed: partial matching is used.
- fitdf
- number of degrees of freedom to be subtracted if
xis 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 null-hypothesis 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 chi-squared
distribution of the test statistic (taking
fitdfinto account. - 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.
"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 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.\ifelse{latex}{\out{~}}{ } 44, 45.
Examples
library(stats)
x <- rnorm (100)
Box.test (x, lag = 1)
Box.test (x, lag = 1, type = "Ljung")