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From GEKS to cycle method

27/06/2017 09:00
The GEKS method and some generalizations are discussed, among them the cycle method.
The paper starts with the standard GEKS method, that is used to transitivize nontransitive price indices. Then several generalizations of the standard method are investigated. These genera-lizations imply that the GEKS method can be used in more cases than in which the standard case can be applied. For instance, the standard GEKS method requires that for each pair of months in the reference period a price should be known. It is shown that this condition can be relaxed if the definition of the GEKS is slightly modified. The standard GEKS method uses geometric averaging. In the paper it is shown that other averaging methods can be used to obtain similar averaged results. Another generalization is to use different weights for the various months in the reference period. This result implies a local form of GEKS, in which only the prices of a neighbourhood of months of a reference month are used instead of the entire reference window. A local GEKS method is thought to be more attractive and flexible than a global one, such as the standard method. GEKS is a bit of a trick that works to produce transitive price indices. But there is no control over the goodness of fit. This would require the use of some kind of metric. In the paper it is shown that it is possible to give such a formulation, however. In fact this leads to the cycle method, another transitivizing method, proposed earlier by the present author.