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

2019/02/08 by Yacouba Boubacar Maïnassara, Maïnassara, Yacouba Boubacar, Abdoulkarim Ilmi Amir +1
Economics, Econometrics and Finance · Social Sciences · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Machine Learning (stat.ML) #Monetary Policy and Economic Impact #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1902.03000

openalex publication_date 2019/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Why Are the ARIMA and SARIMA not Sufficient
• Diagnostic checking of periodic vector autoregressive time series models with dependent errors
• Estimation of weak ARMA models with regime changes
• Estimation of time series models using residuals dependence measures
• On the estimators of autocorrelation model parameters