Since we now have a data base approaching five years of more or less fluctuating exchange rates, there undoubtedly are numerous empirical studies under way comparing the movements of exchange rates with each other and with all sorts of other economic variables. A rather subtle problem with such activities is that the analysis is sensitive to which currency of an exchange rate one chooses to make the numeraire. Specifically, a time series of, say, dollars per pound sterling is not the same thing mathematically as a time series of pounds per dollar although the information content is the same. In particular it can be shown that