  In this paper we consider portmanteau tests for testing the adequacy of
multiplicative seasonal autoregressive moving-average (SARMA) models under the
assumption that the errors are uncorrelated but not necessarily independent.We
relax the standard independence assumption on the error term in order to extend
the range of application of the SARMA models.We study the asymptotic
distributions of residual and normalized residual empirical autocovariances and
autocorrelations underweak assumptions on the noise. We establish the
asymptotic behaviour of the proposed statistics. A set of Monte Carlo
experiments and an application to monthly mean total sunspot number are
presented.
