A portmanteau test is a hypothesis test that jointly examines several time-series autocorrelations. A typical 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.
