ON DISTINGUISHING BETWEEN RANDOM WALK AND CHANGE IN THE MEAN ALTERNATIVES
研究了区分数据序列中结构变化原因的检验方法，特别是区分均值漂移、随机游走和误差结构变化，基于CUSUM统计量并去除均值变化影响后仅对随机游走发散，模拟和德国DAX指数应用验证了方法。
We study test procedures that detect structural breaks in underlying data sequences. In particular, we wish to discriminate between different reasons for these changes, such as (1) shifting means, (2) random walk behavior, and (3) constant means but innovations switching from stationary to difference stationary behavior. Almost all procedures presently available in the literature are simultaneously sensitive to all three types of alternatives. The test statistics under investigation are based on functionals of the partial sums of observations. These cumulative sum–type (CUSUM-type) statistics have limit distributions if the mean remains constant and the errors satisfy the central limit theorem but tend to infinity in the case when any of the alternatives (1), (2), or (3) holds. On removing the effect of the shifting mean, however, divergence of the test statistics will only occur under the random walk behavior, which in turn enables statisticians not only to detect structural breaks but also to specify their causes. The results are underlined by a simulation study and an application to returns of the German stock index DAX.