Premium
Distribution of residual autocorrelations for multiplicative seasonal ARMA models with uncorrelated but nonindependent error terms
Author(s) -
Boubacar Maïnassara Yacouba,
Ilmi Amir Abdoulkarim
Publication year - 2019
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12178
Subject(s) - mathematics , residual , autoregressive model , multiplicative function , statistics , range (aeronautics) , autoregressive–moving average model , independence (probability theory) , econometrics , autocorrelation , monte carlo method , algorithm , mathematical analysis , materials science , composite material
In this paper, we consider portmanteau tests for testing the adequacy of multiplicative seasonal autoregressive moving‐average models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption on the error terms in order to extend the range of applications of the seasonal autoregressive moving‐average models. We study the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations under weak assumptions on noise. We establish the asymptotic behavior of the proposed statistics. A set of Monte Carlo experiments and an application to monthly mean total sunspot number are presented.