# Box.test

0th

Percentile

##### 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 lag autocorrelation coefficients.
type
test to be performed: partial matching is used.
fitdf
number of degrees of freedom to be subtracted if x is 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 "htest" containing the following components:
• statisticthe value of the test statistic.
• parameterthe degrees of freedom of the approximate chi-squared distribution of the test statistic (taking fitdf into account.
• p.valuethe p-value of the test.
• methoda character string indicating which type of test was performed.
• data.namea character string giving the name of the data.

##### Note

Missing values are not handled.

portmanteau

##### 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.44, 45.

• Box.test
##### Examples
library(stats) x <- rnorm (100) Box.test (x, lag = 1) Box.test (x, lag = 1, type = "Ljung")
Documentation reproduced from package stats, version 3.3, License: Part of R 3.3

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