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 (1988 Nature, 334, 613-614) 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 them with those for artificially generated data. Here, we highlight some subtle problems with this approach and suggest possible alternative methods of analysis, especially when the time series of interest are short.