We propose a new unit-root test based on Lagrange Multipliers, where we extend the null hypothesis to an integrated moving-average process (IMA(1,1)) and the alternative to a first-order threshold autoregressive moving-average process (TARMA(1,1)). This new theoretical framework provides tests with good size without pre-modelling steps. Moreover, leveraging on the versatile capability of the TARMA(1,1), our test has power against a wide range of linear and nonlinear alternatives. We prove the consistency and asymptotic similarity of the test. The proof of tightness of the test is of independent and general theoretical interest. Moreover, we propose a wild bootstrap version of the statistic. Our proposals outperform most existing tests in many contexts. We support the view that rejection does not necessarily imply nonlinearity so that unit-root tests should not be used uncritically to select a model. Finally, we present an application to real exchange rates.

翻译：我们建议基于拉格朗多端利差的新单位根试验, 将无效假设扩展至综合移动平均过程( IMA(1, 1) 和第一阶阈值自动递减平均过程的替代方法( TARMA(1, 1) ) 。 这个新的理论框架提供了良好的试验, 但没有预先设计步骤。 此外, 利用TARMA( 1, 1) 的多功能能力, 我们的试验具有对抗广泛的线性和非线性替代方法的力量。 我们证明了试验的一致性和无孔不入的相似性。 测试的紧凑性证据是独立和普遍的理论利益。 此外, 我们提出了统计学的野生靴套式版本。 我们的提议在许多情形下优于大多数现有的试验。 我们支持这样的观点, 拒绝并不一定意味着非线性, 这样单位根试验就不应该被不严格地用于选择模型。 最后, 我们提出了实际汇率的应用 。