In this paper several indices are explored that are based on the idea of decomposing prices or volumes and quantities, into a time component and a goods component.
Our interest is in the time component which is viewed as a price index; the goods component is a nuisance parameter. The indices we consider can be viewed as derivatives of an idealized price index of the Geary-Khamis type. Among the derivatives there is the time product dummy index. There are several others which also may be of interest. In particular we look at an incremental price index, which could be used for a flash HICP, using both past and recent data. We also consider conditions for the existence of a GK index.