TESTING STRUCTURAL CHANGE IN PARTIALLY LINEAR MODELS
针对部分线性时间序列模型，提出了两种结构变化检验方法，分别检验参数分量和参数与非参数分量的同时变化，并推导了极限分布，通过蒙特卡洛模拟验证了有限样本性质。
We consider two tests of structural change for partially linear time-series models. The first tests for structural change in the parametric component, based on the cumulative sums of gradients from a single semiparametric regression. The second tests for structural change in the parametric and nonparametric components simultaneously, based on the cumulative sums of weighted residuals from the same semiparametric regression. We derive the limiting distributions of both tests under the null hypothesis of no structural change and for sequences of local alternatives. We show that the tests are generally not asymptotically pivotal under the null but may be free of nuisance parameters asymptotically under further asymptotic stationarity conditions. Our tests thus complement the conventional instability tests for parametric models. To improve the finite-sample performance of our tests, we also propose a wild bootstrap version of our tests and justify its validity. Finally, we conduct a small set of Monte Carlo simulations to investigate the finite-sample properties of the tests.