Testing for shifts in mean with monotonic power against multiple structural changes

It is known that several widely used structural change tests have non-monotonic power because the long-run variance is poorly estimated under the alternative hypothesis. In this paper, we propose a modified long-run variance estimator to alleviate this problem. We theoretically show that the tests with our long-run variance estimator are consistent against large multiple structural changes. Simulation results show that the proposed test performs well in finite samples.众所周知，多款广泛应用的结构变化检验（structural change tests）存在非单调检验势（non-monotonic power）问题，其根源在于备择假设（alternative hypothesis）下的长期方差（long-run variance）估计效果不佳。本文提出一种改进型长期方差估计量（modified long-run variance estimator）以缓解该类问题。我们通过理论推导证明，搭载本文提出的长期方差估计量的结构变化检验，在存在多重显著结构变化的备择情形下仍具备一致检验特性。模拟实验结果表明，本文提出的检验方法在有限样本（finite samples）情境下表现优异。