Goodness-of-fit tests in long-range dependent processes under fixed alternatives

In a recent paper Fay and Philippe (2002) proposed a goodness-of-fit test for long-range dependent processes which uses the logarithmic contrast as information measure. These authors established asymptotic normality under the null hypothesis and local alternatives. In the present note we extend these results and show that the corresponding test statistic is also normally distributed under fixed alternatives. AMS Subject Classi cation: 60F05, 62F0