THE LOCAL ASYMPTOTIC POWER OF CERTAIN TESTS FOR FRACTIONAL INTEGRATION
证明基于时间序列部分和过程的分数积分检验（如重标极差检验）对局部备择假设只有平凡渐近势，即检验功效等于显著性水平，说明这类检验在实证中效果不佳。
It is possible to construct a test of the null of no fractional integration that has nontrivial asymptotic power against a sequence of alternatives specifying that the series is I ( d ) with d = O ( T −1/2 ), where T is the sample size. In this paper, I show that tests for fractional integration that are based on the partial sum process of the time series have only trivial asymptotic power (i.e., equal to the size) against this sequence of local alternatives. These tests include the rescaled-range test. In this sense, despite its widespread use in empirical work, the rescaled-range test is a poor test for fractional integration.