Testing for the Presence of a Random Walk in Series with Structural Breaks
本文提出了在存在结构断点的时间序列中检验随机游走成分的方法，包括局部最优不变检验和修正检验统计量，其渐近分布不依赖于断点位置，并通过模拟和实际数据（尼罗河流量、美国GNP）验证了性能。
We consider tests for the presence of a random walk component in a stationary or trend stationary time series and extend them to series that contain structural breaks. The locally best invariant (LBI) test is derived and the asymptotic distribution is obtained. Then a modified test statistic is proposed. The advantage of this statistic is that its asymptotic distribution is not dependent on the location of the break point and its form is that of the generalized Cramer–von Mises distribution, with degrees of freedom depending on the number of break points. The performance of this modified test is shown, via some simulation experiments, to be comparable with that of the LBI test. An unconditional test, based on the assumption that there is a single break at an unknown point, is also examined. The use of the tests is illustrated with data on the flow of the Nile and US gross national product.