SummaryThis paper considers a moderately explosive AR(1) process where the autoregressive root approaches unity from the right at a certain rate. We first develop a test for the null of moderate explosiveness under independent and identically distributed errors. We show that the t statistic is asymptotically standard normal regardless of whether the true process is dominated by the stochastic moderately explosive trend or the deterministic nonlinear drift trend. This result is in sharp contrast with the existing literature, wherein nonstandard limiting distributions are obtained under different model assumptions. When the errors are weakly dependent, we show that the t statistic based on a heteroskedasticity and autocorrelation robust standard error follows Student’s t distribution in large samples. Monte Carlo simulations show that our tests have satisfactory size and power performances in finite samples. Applying the asymptotic t test to ten major stock indexes in the pre-2008 financial exuberance period, we find that most indexes are only mildly explosive or not explosive at all, which implies that the bout of the irrational rise was not as serious as previously thought.

中文翻译：

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测试中度爆炸性

结束语本文考虑了一个中等爆炸性AR（1）过程，其中自回归根以一定速率从右趋于统一。我们首先针对独立且分布均匀的误差，针对中等爆炸性的零值进行测试。我们表明，t统计量是渐近标准正态的，无论真实过程是由随机的适度爆炸性趋势还是确定性非线性漂移趋势主导。该结果与现有文献形成了鲜明的对比，在现有文献中，在不同的模型假设下获得了非标准的极限分布。当误差是弱相关的时，我们表明基于异方差性和自相关鲁棒标准误差的t统计量在大样本中遵循Student的t分布。蒙特卡洛仿真表明，我们的测试在有限的样本中具有令人满意的尺寸和功率性能。将渐进t检验应用于2008年之前的金融繁荣时期的十种主要股指，我们发现大多数指数只是轻微爆发性或根本没有爆发性，这表明非理性上涨的回合并不像以前认为的那么严重。 。