A Model‐Adaptive Test for Parametric Single‐Index Time Series Models
提出一种模型自适应降维检验方法，用于验证参数化单指标时间序列模型的复合结构，能同时适应原假设和备择假设，提升检验功效。
In this paper, based on certain residual‐marked empirical processes, we study the model test to validate the composite structure with a given link function for parametric single‐index time series models. To extend an existing directional test that avoids the curse of dimensionality to an omnibus test, a model‐adaptive dimension‐reduction test procedure is proposed. Moreover, to fully utilize the dimension‐reduction structure under the null hypothesis, the test is designed for adapting both the null and alternative hypotheses, which can improve the power for a more general alternative. Simulation results and a real data example show that the proposed method can perform effectively in checking parametric single‐index time series models.