存在测量误差时阈值调节的检验及对PPP假设的应用
Testing for threshold regulation in presence of measurement error with an application to the PPP hypothesis
摘要：
调节是表征许多动力学现象的重要特征，并且可以在阈值自回归设置内进行测试，其中原假设是全局非平稳过程。尽管如此，这种设置是有争议的，因为数据经常被测量误差破坏。因此，它是更合适的考虑阈值自回归移动平均模型作为一般的假设。我们实现了这个新的设置与集成的移动平均模型的一阶为原假设。我们推导出一个拉格朗日乘子检验，它具有渐近相似的零分布，并提供了第一个严格的证明，有关测试阈值非线性对差异平稳性，这是独立的利益的紧密性。仿真研究表明，当存在测量误差时，该方法比现有的阈值调节检测方法具有更小的偏差和更高的功率。我们将新方法应用于欧元区国家的每日实际汇率。它支持购买力平价假说，通过一个非线性的均值回复机制，在越过位于极端上尾的阈值时触发。此外，我们分析了欧元区的系列，并提出了一个阈值自回归移动平均规格，这揭示了新的购买力平价辩论。
英文摘要：
Regulation is an important feature characterising many dynamical phenomena and can be tested within the threshold autoregressive setting, with the null hypothesis being a global non-stationary process. Nonetheless, this setting is debatable since data are often corrupted by measurement errors. Thus, it is more appropriate to consider a threshold autoregressive moving-average model as the general hypothesis. We implement this new setting with the integrated moving-average model of order one as the null hypothesis. We derive a Lagrange multiplier test which has an asymptotically similar null distribution and provide the first rigorous proof of tightness pertaining to testing for threshold nonlinearity against difference stationarity, which is of independent interest. Simulation studies show that the proposed approach enjoys less bias and higher power in detecting threshold regulation than existing tests when there are measurement errors. We apply the new approach to the daily real exchange rates of Eurozone countries. It lends support to the purchasing power parity hypothesis, via a nonlinear mean-reversion mechanism triggered upon crossing a threshold located in the extreme upper tail. Furthermore, we analyse the Eurozone series and propose a threshold autoregressive moving-average specification, which sheds new light on the purchasing power parity debate.
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