摘要翻译：
规律性是表征许多动力学现象的一个重要特征，可以在零假设为全局非平稳过程的阈值自回归条件下进行检验。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，将门限自回归滑动平均模型作为一般假设更为合适。我们用一阶综合移动平均模型作为零假设来实现这个新的设置。我们导出了一个具有渐近相似零分布的拉格朗日乘子检验，并给出了门限非线性与差分平稳性检验的第一个严格的严密性证明。仿真研究表明，当存在测量误差时，该方法比现有的检测方法具有更小的偏差和更高的检测阈值调节能力。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，我们分析了欧元区序列，并提出了一个阈值自回归移动平均规范，这为购买力平价辩论提供了新的线索。
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英文标题：
《Testing for threshold regulation in presence of measurement error with
  an application to the PPP hypothesis》
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作者：
Kung-Sik Chan, Simone Giannerini, Greta Goracci, Howell Tong
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最新提交年份：
2021
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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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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PDF链接：
https://arxiv.org/pdf/2002.09968