Diagnostic Checking in Multivariate ARMA Models With Dependent Errors Using Normalized Residual Autocorrelations
推导了弱假设下标准化残差经验自协方差和自相关的渐近分布，提出了针对非独立新息向量自回归移动平均模型的新混成检验统计量，并通过蒙特卡洛实验和CAC40日收益率数据验证。
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.