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Testing for moderate explosiveness

机译：测试适度爆炸物

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This 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.
机译：本文考虑了一个适度爆炸性的AR（1）过程，自回归根以一定的速率从右侧接近统一。我们首先在独立和相同分布的错误下开发了对中等爆炸性的NULL的测试。我们表明，无论真正的过程是由随机中等爆炸性趋势还是确定性非线性漂移趋势，T统计数据都是渐近标准的正常。该结果与现有文献形成鲜明对比，其中在不同的模型假设下获得非标准限制分布。当错误依赖时，我们表明，基于异质性能和自相关的T统计数据持有稳健的标准误差遵循大型样品中的学生的T分布。 Monte Carlo模拟表明，我们的测试在有限样本中具有令人满意的尺寸和功率性能。将渐近T检验应用于2008年金融繁荣期的十大股指，我们发现大多数指数都只是轻微的爆炸性或根本不爆炸，这意味着非理性崛起的回合并不像以前一样严重。 。

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