PARAMETRIC SPECIFICATION TEST FOR NONLINEAR AUTOREGRESSIVE MODELS
提出一种检验非线性自回归模型条件均值和方差参数设定的方法，通过比较两种密度估计的收敛速度差异，在阈值自回归和条件异方差模型中验证了有效性。
The paper considers testing parametric assumptions on the conditional mean and variance functions for nonlinear autoregressive models. To this end, we compare the kernel density estimate of the marginal density of the process with a convolution-type density estimate. It is shown that, interestingly, the latter estimate has a parametric $\left( {\sqrt n } \right)$ rate of convergence, thus substantially improving the classical kernel density estimates whose rates of convergence are much inferior. Our results are confirmed by a simulation study for threshold autoregressive processes and autoregressive conditional heteroskedastic processes.