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box.test 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 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:

statistic	the value of the test statistic.
parameter	the degrees of freedom of the approximate chi-squared distribution of the test statistic (taking fitdf into 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.

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")