A unit root test is proposed for time series with a general nonlinear deterministic trend component. It is shown that asymptotically the pooled OLS estimator of overlapping blocks filters out any trend component that satisfies some Lipschitz condition. Under both fixed-$b$ and small-$b$ block asymptotics, the limiting distribution of the t-statistic for the unit root hypothesis is derived. Nuisance parameter corrections provide heteroskedasticity-robust tests, and serial correlation is accounted for by pre-whitening. A Monte Carlo study that considers slowly varying trends yields both good size and improved power results for the proposed tests when compared to conventional unit root tests.

中文翻译：

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具有缓慢变化趋势的单位根检验

建议对具有一般非线性确定性趋势分量的时间序列进行单位根检验。结果表明，重叠块的池化 OLS 估计器逐渐过滤掉满足某些 Lipschitz 条件的任何趋势分量。在固定-$b$ 和小-$b$ 块渐近下，导出了单位根假设的t 统计量的极限分布。Nuisance 参数校正提供了异方差稳健性测试，并且通过预白化来解释序列相关性。与传统单位根检验相比，考虑缓慢变化趋势的蒙特卡罗研究为所提议的检验产生了良好的规模和改进的功效结果。