 For example, for an ARIMA(p,0,q) model, the degrees of freedom should be set to formula_7.The Box-Pierce test uses the test statistic, in the notation outlined above, given by
and it uses the same critical region as defined above.Simulation studies have shown that the distribution for the Ljung–Box statistic is closer to a formula_4 distribution than is the distribution for the Box-Pierce statistic for all sample sizes including small ones.