An Improvement of the Portmanteau Statistic

.  The portmanteau statistic is based on the first m ‐residual autocorrelations, and is used for diagnostic checks on the adequacy of fit of a model. In this article, we propose a modified portmanteau statistic with a correction term that allows for the use of small values of m for the chi‐squared test. For this modification, we take a different approach to that suggested by Ljung [ Biometrika (1986), Vol. 73, pp. 725–30]. Their empirical behaviour is clarified using asymptotic theory.