A portmanteau test is a statistical test that jointly examines several time-series autocorrelations. A typical test statistic has the form
 |
where 
is the sample autocorrelation at lag 
and the weights 
depend on the particular test. Under the null
hypothesis that the tested autocorrelations
are zero, 
is commonly compared with a chi-squared distribution.
For fitted-model residuals, the degrees of freedom are adjusted to account for estimated
model parameters.
The Box-Pierce test uses 
, while the Ljung-Box test
uses a finite-sample correction.
