The Coefficient of Variation (CV) is a heuristic measure of variability
comparing samples with different means. I was asked to suggest a
measure of variability for non-stationary data where the series may have
different ranges but are measured over the same timespans. It seems to
me that having fit some model to the data series, the sqrt(MSE) is
analogous to the SD, and sqrt(MSE)/mean can be used heuristically, at
least to rank: 100 +/-20 is less variable than 50 +/-20. The mean is,
here, purely the sample mean and not an estimate of any population
parameter, but this seems to separate any "strength of trend" and
"variability round expectation" for reporting.
Are there prior examples of sqrt(MSE)/mean for non-stationary data, or
do colleagues have methodological objections?
Allan
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