On multiple portmanteau tests*

Abstract. The portmanteau statistic based on the first m residual autocorrelations is used for diagnostic checks on the adequacy of fitting a model with varying m. In this article, we propose an approximation of the joint probability of multiple portmanteau tests with different degrees of freedom (DF). This distribution is easy to compute when all DF are even integers; its empirical behaviour is clarified in terms of asymptotic theory.