Significance levels of the Box-Pierce portmanteau statistic in finite samples

In time series model building, using the methodology of Box & Jenkins (1970), it is usual to verify the adequacy of a fitted equation by computing residual autocorrelations. Following Box & Pierce (1970), an overall, or ’portmanteau’, test of fit can be based on these quantities. Recent experience suggests that surprisingly low values of the portmanteau statistic are often found. This paper shows that, even for moderately large sample sizes, the true significance levels are likely to be much lower than predicted by asymptotic theory.