Extremal Dependence-Based Specification Testing of Time Series
提出一种基于标准化残差极值相依性的条件位置-尺度模型设定检验，通过比较残差在不同滞后期的尾部相依性与独立情形下的差异来构造检验统计量，该统计量渐近分布不含冗余参数，计算简便，且能检测出传统自相关检验无法发现的残差序列依赖问题。
We propose a specification test for conditional location–scale models based on extremal dependence properties of the standardized residuals. We do so comparing the left-over serial extremal dependence—as measured by the pre-asymptotic tail copula—with that arising under serial independence at different lags. Our main theoretical results show that the proposed Portmanteau-type test statistics have nuisance parameter-free asymptotic limits. The test statistics are easy to compute, as they only depend on the standardized residuals, and critical values are likewise easily obtained from the limiting distributions. This contrasts with some extant tests (based, e.g., on autocorrelations of squared residuals), where test statistics depend on the parameter estimator of the model and critical values may need to be bootstrapped. We show that our tests perform well in simulations. An empirical application to S&P 500 constituents illustrates that our tests can uncover violations of residual serial independence that are not picked up by standard autocorrelation-based specification tests, yet are relevant when the model is used for, for example, risk forecasting.