This paper studies large sample properties of a moderately explosive autoregression with a structural change in the unobservable drift term, and develops asymptotic tests for the null of moderate explosiveness under different dependence structures. When the innovation sequence is independently and identically distributed (i.i.d.), we show that the t statistic is asymptotically standard normal. When the innovations are weakly dependent in the form of homoskedasticity or conditional heteroskedasticity, we invoke the fixed-smoothing asymptotics to construct the heteroskedasticity and autocorrelation robust standard error, under which the t statistic follows Student’s t distribution in large samples. Monte Carlo simulations show that our tests have small size distortion and high power in finite samples. As we impose no restrictions on the occurrence time and magnitude of the drift, our proposed asymptotic tests enjoy strong robustness and applicability.

中文翻译：

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测试具有漂移结构变化的中度爆炸过程*

本文研究了具有不可观测漂移项结构变化的中度爆炸性自回归的大样本性质，并开发了不同依赖结构下中度爆炸性零点的渐近检验。当创新序列独立同分布（iid）时，我们证明t统计量是渐近标准正态的。当创新以同方差或条件异方差的形式弱依赖时，我们调用固定平滑渐近法来构建异方差和自相关稳健标准误差，在此条件下t统计量遵循学生t大样本分布。蒙特卡罗模拟表明，我们的测试在有限样本中具有小尺寸失真和高功效。由于我们对漂移的发生时间和幅度没有限制，我们提出的渐近测试具有很强的鲁棒性和适用性。