摘要
本文研究参数单指标时间序列分位数自回归模型有效性的检验问题.当分位数回归变量的维数较大时,现有的检验方法将面临"维数灾难"问题.为了解决这个问题,本文基于残差经验过程,利用降维思想构造统计量,它有效地适应于参数单指标时间序列分位数自回归模型.本文提出Khmaladze鞅转换方法来替代经验过程,并构造检验统计量,证明所构造的检验统计量能够渐近收敛到分布自由的标准Brown运动.模拟研究和实际数据分析的结果表明,本文所提方法在参数单指标分位数自回归模型的检验中优于已有的检验方法.
In this paper, we study the nonparametric tests for the validity of the parametric single-index time series quantile autoregression with a given parametric link function. When the dimension of the quantile regressors is large, the existing tests will face the "curse of dimensionality" problem. To solve this problem, we utilize a dimension reduction idea, which perfectly adapts to parametric single-index time series, based on certain empirical processes marked by the residuals. We use the Khmaladze transformation to replace the underlying test process by its martingale part, and then the resulting test statistic is an asymptotically distribution-free test related to a standard Brownian motion. The simulation results and a real data example show that the proposed method performs better than the existing methods in checking parametric single-index quantile autoregression.
引文
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