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Unit root tests in three-regime SETAR models

机译：三体制SETAR模型中的单位根检验

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摘要

This paper proposes a simple testing procedure to distinguish a unit root process from a globally stationary three-regime self-exciting threshold autoregressive process. Following the threshold cointegration literature we assume that the process follows the random walk in the corridor regime, and therefore we propose that the null of a unit root be tested by the Wald statistic for the joint significance of autoregressive parameters in both lower and upper regimes. We establish that when threshold parameters are known, the suggested Wald test has a well-defined asymptotic null distribution free of nuisance parameters. In the general case where threshold parameters are unknown a priori, we consider the three most commonly used summary statistics based on their average, exponential average and supremum. Assuming that the grid set for thresholds can be selected such that the corridor regime be of finite width both under the null and under the alternative, we can establish both stochastic equicontinuity and uniform convergence of the aforementioned summary statistics. Monte Carlo evidence indicates that the proposed tests are more powerful than the Dickey-Fuller test that ignores the threshold nature under the alternative. We illustrate the usefulness of our proposed tests by examining stationarity of real exchange rates for the G7 countries.
机译：本文提出了一种简单的测试程序，以将单位根过程与全局平稳的三态自激阈值自回归过程区分开。根据阈值协整文献，我们假设该过程遵循走廊制度中的随机游动，因此，我们建议由Wald统计量检验单位根的零值，以了解上下制度中自回归参数的联合显着性。我们确定，当阈值参数已知时，建议的Wald检验具有无干扰参数的明确定义的渐近零分布。在先验阈值参数未知的一般情况下，我们根据其平均值，指数平均值和极值来考虑三种最常用的汇总统计量。假设可以选择阈值的网格集，以使走廊状态在零值和替代状态下都具有有限的宽度，我们可以建立上述摘要统计量的随机等连续性和统一收敛性。蒙特卡洛证据表明，所提出的测试比忽略Dickey-Fuller测试的阈值性质更强大。我们通过检验七国集团（G7）国家实际汇率的平稳性来说明我们提出的测试的有用性。

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