Self‐normalization inference for linear trends in cointegrating regressions
针对协整回归中随机解释变量带有确定性线性趋势的情况，提出了基于自标准化方法的趋势系数检验，无需异方差自相关一致估计，模拟显示该方法在控制尺寸扭曲方面表现最优。
In this article, statistical tests concerning the trend coefficient in cointegrating regressions are addressed for the case when the stochastic regressors have deterministic linear trends. The self‐normalization (SN) approach is adopted for developing inferential methods in the integrated and modified ordinary least squares (IMOLS) estimation framework. Two different self‐normalizers are used to construct the SN test statistics: a functional of the recursive IMOLS estimators and a functional of the IMOLS residuals. These two self‐normalizers produce two SN tests, denoted by and respectively. Neither test requires studentization with a heteroskedasticity and autocorrelation consistent (HAC) estimator. A trimming parameter must be chosen to implement the test, whereas the test does not require any tuning parameter. In the simulation, the test exhibits the smallest size distortion among the inferential methods examined in this article. However, this may come with some loss of power, particularly in small samples.