A critical look at Lo's modified R/S statistic

We report on an empirical investigation of the modified rescaled adjusted range or RIS statistic that was proposed by Lo, 1991. Econometrica 59, 1279-1313, as a test for long-range dependence with good robustness properties under `extra' short-range dependence. In contrast to the classical RIS statistic that uses the standard deviation S to normalize the rescaled range R, Lo's modified R/S-statistic V(q) is normalized by a modified standard deviation S(q) which takes into account the covariances of the first q lags, so as to discount the influence of the short-range dependence structure that might be present in the data. Depending on the value of the resulting test-statistic V(q), the null hypothesis of no long-range dependence is either rejected or accepted. By performing Monte-Carlo simulations with `truly' long-range- and short-range dependent time series, we study the behavior of V(q), as a function of q, and uncover a number of serious drawbacks to using Lo's method in practice. For example, we show that as the truncation lag q increases, the test statistic V(q) has a strong bias toward accepting the null hypothesis (i.e., no long-range dependence), even in ideal situations of `purely' long-range dependent data. (C) 1999 Elsevier Science B.V. All rights reserved.