标题： 非平稳时间序列回归的非参数规范 显示英文标题

标题： Nonparametric specification for non-stationary time series regression

摘要： 我们研究了广义似然比检验（GLRT）（Fan、Zhang 和 Zhang [Ann. Statist. 29 (2001) 153-193]）在回归变量和误差项均为非平稳时间序列且可能存在交叉相关性的时间变系数模型中的行为。结果表明，在弱相关性和非平稳性条件下，GLRT 保留了局部替代检测的 minimax 速率。然而，一般来说，经典的威尔克斯现象以及经典残差自助法对误差的条件异方差性、非平稳性或时间依赖性非常敏感。建议使用平均检验来缓解检验对带宽选择的敏感性，并证明其比基于单一带宽的检验更强大。提出了一种替代的野-bootstrap 方法，并证明当对非平稳时间序列的时间变系数模型进行推断时，该方法是一致的。 显示英文摘要

摘要： We investigate the behavior of the Generalized Likelihood Ratio Test (GLRT) (Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193]) for time varying coefficient models where the regressors and errors are non-stationary time series and can be cross correlated. It is found that the GLRT retains the minimax rate of local alternative detection under weak dependence and non-stationarity. However, in general, the Wilks phenomenon as well as the classic residual bootstrap are sensitive to either conditional heteroscedasticity of the errors, non-stationarity or temporal dependence. An averaged test is suggested to alleviate the sensitivity of the test to the choice of bandwidth and is shown to be more powerful than tests based on a single bandwidth. An alternative wild bootstrap method is proposed and shown to be consistent when making inference of time varying coefficient models for non-stationary time series.