The statistical properties of ecological time-series data and general
trends therein have historically been of great interest to ecologists.
In recent years, there has been a focus on establishing the relative importance
of ``memory'' in these data. The classic study by Pimm & Redfearn
has been extremely important in establishing within the ecological community
the idea that population time-series are generally ``red-shifted'' (dominated
by long-term trends). This conclusion was reached by exploring the
relationship between observed variability and census length in ecological
data and comparing these observed patterns with those for artificially
generated data. Here, we highlight some subtle problems with this statistical
approach and suggest possible alternative methods of analysis, especially
when the time-series of interest are short.