Portmanteau tests for periodic ARMA models with dependent errors
研究了误差相关但不独立时周期自回归移动平均模型的残差自协方差和自相关的渐近分布，提出了修正的混合检验统计量，并基于自归一化方法给出另一种检验，通过蒙特卡洛实验和金融数据应用验证。
In this article, we derive the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations of (parsimonious) periodic autoregressive moving‐average (PARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We then deduce the modified portmanteau statistics. We establish the asymptotic behavior of the proposed statistics. It is shown that the asymptotic distribution of the modified portmanteau tests is that of a weighted sum of independent chi‐squared random variables, which can be different from the usual chi‐squared approximation used under independent and identically distributed assumption on the noise. We also propose another test based on a self‐normalization approach to check the adequacy of PARMA models. A set of Monte Carlo experiments and an application to financial data are presented.