Distribution of residual autocorrelations for multiplicative seasonal ARMA models with uncorrelated but non-independent error terms
This work extends the applicability of SARMA models to cases with non-independent errors, which is incremental for time series analysis in fields like climatology.
The paper tackles the problem of testing the adequacy of multiplicative seasonal ARMA models when errors are uncorrelated but not necessarily independent, and it establishes the asymptotic distributions of residual autocorrelations and presents Monte Carlo experiments and an application to sunspot data.
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.