# Distribution of residual autocorrelations for multiplicative seasonal ARMA models with uncorrelated but non-independent error terms

## TL;DR

This paper extends portmanteau tests for SARMA models by relaxing the independence assumption on errors, analyzing residual autocorrelations under weaker conditions, and validating findings through simulations and real data application.

## Contribution

It introduces new asymptotic results for residual autocorrelations in SARMA models with uncorrelated but dependent errors, broadening their applicability.

## Key findings

- Asymptotic distributions of residual autocorrelations are derived.
- Monte Carlo experiments validate the theoretical results.
- Application to sunspot data demonstrates practical relevance.

## Abstract

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.