In this paper, we propose an adaptive group lasso procedure to efficiently estimate structural breaks in cointegrating regressions. It is well-known that the group lasso estimator is not simultaneously estimation consistent and model selection consistent in structural break settings. Hence, we use a first step group lasso estimation of a diverging number of breakpoint candidates to produce weights for a second adaptive group lasso estimation. We prove that parameter changes are estimated consistently by group lasso and show that the number of estimated breaks is greater than the true number but still sufficiently close to it. Then, we use these results and prove that the adaptive group lasso has oracle properties if weights are obtained from our first step estimation. Simulation results show that the proposed estimator delivers the expected results. An economic application to the long-run US money demand function demonstrates the practical importance of this methodology.
翻译:在本文中,我们提出一个适应性分组拉索程序,以有效估计整合回归过程中的结构间断。众所周知,该组拉索估计值并不是同时估算一致性,而模型选择在结构间断设置中是一致的。因此,我们使用对不同断点候选人的分数的分数进行第一步分组估计,以产生第二个适应性分组拉索估计的权重。我们证明参数变化是按组拉索一致估算的,并表明估计的间断数大于实际数,但仍与实际数相当。然后,我们利用这些结果来证明适应性组合拉索如果从第一步估计中获得权重,则具有骨骼特性。模拟结果显示,拟议的估计值提供了预期结果。美国长期资金需求功能的经济应用证明了这一方法的实际重要性。