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.

`Box.test(x, lag = 1, type = c("Box-Pierce", "Ljung-Box"), fitdf = 0)`

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.

A list with class `"htest"`

containing the following components:

the value of the test statistic.

the degrees of freedom of the approximate chi-squared
distribution of the test statistic (taking `fitdf`

into account).

the p-value of the test.

a character string indicating which type of test was performed.

a character string giving the name of the data.

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`

.

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.
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.
10.2307/2335207.

Harvey, A. C. (1993)
*Time Series Models*.
2nd Edition, Harvester Wheatsheaf, NY, pp.44, 45.

# NOT RUN { x <- rnorm (100) Box.test (x, lag = 1) Box.test (x, lag = 1, type = "Ljung") # }