The paper criticizes the translation of the so called GEKS (Gini - Eltetö - Köves - Szulc) method to make consistent (transitive, or "drift free") international comparisons of price indices (parities), into the intertemporal framework. It shows that transitivity appears to be "over-ambitious" and too restrictive in this context, where chain indices possibly may suffice. Formulas of GEKS indices are complicated geometric averages of many (2m-3) direct Fisher indices relating to m periods in time. They are therefore much more difficult to compile in praxis than both, chained and direct Fisher indices. They are only transitive for a given m, but as we are free to choose different m's there is no unique, "drift free" index to compare any two periods, s and t. Instead there are many indices Pst depending on m. Moreover with new periods, t+1, t+2, … the method requires an updating (as m increases) and a re-computing of all previously compiled indices Pst. With chain indices the update is much easier and there is no need for a re-computing. To avoid such problems a "rolling" variant (RGEKS), a kind of moving average methodology, has been proposed. With RGEKS (of which chain indices are the limiting case of m = 2), however, desirable properties of (standard) GEKS, such as transitivity and proportionality get lost, and with a cyclical movement in the prices we can well generate a trend in the indices which is absent in the underlying price data.