# box.test: Box-Pierce and Ljung-Box Tests

Description Usage Arguments Details Value Note Author(s) References Examples

## 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

 `1` ```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.

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. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_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. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("10.2307/2335207")}.

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

## Examples

 ```1 2 3``` ```x <- rnorm (100) Box.test (x, lag = 1) Box.test (x, lag = 1, type = "Ljung") ```