标题： 基于 GCov 的拟合优度检验 显示英文标题

标题： GCov-Based Portmanteau Test

摘要： 我们研究基于包含非线性自协方差的端粒统计量的非高斯时间序列和动态模型残差的非线性序列依赖检验。 引入了一种渐近分布为$\chi^2$的新检验方法，用于检验时间序列中的非线性序列依赖（NLSD）。 该检验受到最近提出的基于广义协方差（GCov）残差的规范检验的启发，作为具有独立同分布非高斯误差的半参数动态模型的诊断工具。 当模型正确设定并由 GCov 估计器估计时，它服从$\chi^2$分布。 我们在局部替代条件下推导了关于半参数模型参数的假设检验的新渐近结果。 我们通过引入一种 GCov 引导检验用于残差诊断，\color{black}，该检验也可用于通过其他方法估计的模型，例如在误差分布有参数假设下的最大似然估计器。 \color{black}模拟研究表明，这些检验在混合因果-非因果自回归模型的应用中表现良好。 GCov 规范检验用于评估铝价混合因果-非因果模型的拟合度，即 2005 年至 2024 年间的局部爆炸模式，即泡沫和尖峰。 显示英文摘要

摘要： We study nonlinear serial dependence tests for non-Gaussian time series and residuals of dynamic models based on portmanteau statistics involving nonlinear autocovariances. A new test with an asymptotic $\chi^2$ distribution is introduced for testing nonlinear serial dependence (NLSD) in time series. This test is inspired by the Generalized Covariance (GCov) residual-based specification test, recently proposed as a diagnostic tool for semi-parametric dynamic models with i.i.d. non-Gaussian errors. It has a $\chi^2$ distribution when the model is correctly specified and estimated by the GCov estimator. We derive new asymptotic results under local alternatives for testing hypotheses on the parameters of a semi-parametric model. We extend it by introducing a GCov bootstrap test for residual diagnostics,\color{black} which is also available for models estimated by a different method, such as the maximum likelihood estimator under a parametric assumption on the error distribution. \color{black} A simulation study shows that the tests perform well in applications to mixed causal-noncausal autoregressive models. The GCov specification test is used to assess the fit of a mixed causal-noncausal model of aluminum prices with locally explosive patterns, i.e. bubbles and spikes between 2005 and 2024.