Diagnostic Checking in Multivariate ARMA Models With Dependent Errors Using Normalized Residual Autocorrelations

• 成果类型: Article
• 署名作者: Mainassara, Yacouba Boubacar; Saussereau, Bruno
• 署名单位: Universite Marie et Louis Pasteur
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1380030
• 发表日期: 2018
• 页码: 1813-1827
• 关键词: structural varma models; time-series models; heteroskedasticity; estimators; inference

摘要

In this paper, we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We propose new portmanteau statistics for vector autoregressive moving average models with uncorrelated but nonindependent innovations by using a self-normalization approach. We establish the asymptotic distribution of the proposed statistics. This asymptotic distribution is quite different from the usual chi-squared approximation used under the independent and identically distributed assumption on the noise, or the weighted sum of independent chi-squared random variables obtained under nonindependent innovations. A set of Monte Carlo experiments and an application to the daily returns of the CAC40 is presented. Supplementary materials for this article are available online.