  Under long memory, the limit theorems for normalized sums of random variables
typically involve a positive integer called "Hermite rank". There is a
different limit for each Hermite rank. From a statistical point of view,
however, we argue that a rank other than one is unstable, whereas, a rank equal
to one is stable. We provide empirical evidence supporting this argument. This
has important consequences. Assuming a higher-order rank when it is not really
there usually results in underestimating the order of the fluctuations of the
statistic of interest. We illustrate this through various examples involving
the sample variance, the empirical processes and the Whittle estimator.
