derivation, were previously available from the St. Louis Federal Reserve Bank. Those aggregates, along with newer extensions, are now available from the Center for Financial Stability in New York City. Some price indexes incorporate changes in the quantity, expenditure share, and quality on various underlying goods as well as the changes in prices for them, although the term Divisia index is not often used in the official descriptions of consumer price indexes, producer price indexes, or personal consumption indexes. Various price indexes use the Törnqvist, Fisher-Ideal, or other procedures which produce close approximations to a Divisia index. Data input The theory of the Divisia indexes of goods (say, inputs to a production process, or prices for consumer goods) uses these components as data input: there are n inputs, where n is a whole number t is a continuous index of time, starting at 0 are continuous series of price data for each input from i=1 to i=n are continuous series of quantity data for each input. The shifting importance of the various goods are measured, for prices, by the changes in quantities, and for quantities by the changes in prices. One might therefore use something different from literal price or quantity to measure these importance/weights. Arbitrary index based levels P(0) and Q(0) are selected -- in practice, 1, or 100, or one is chosen in this way and the other is chosen to meet the criteria that P(0)*Q(0) equals the actual amount of the transactions, or value, exchanged: Then a price index P(t) and quantity index Q(t) are the solution to a differential equation and if P(0) and Q(0) were chosen suitably the series summarize all transactions in the sense that for all t: Discrete-time approximations In practices, discrete time analogues to Divisia indexes are the ones computed and used. To define and compute changes in a discrete time index closely analogous to a Divisia index from time 0 to time 1: Gather price and quantity for each component, using measures that have been adjusted for quality change if possible Compute cost/price/expenditure fractions for each component at time 1 and time 2. Average the time-1 and time-2 fractions for each component. Use those averages as the 'weights' for the component. Define the weights to be averages of expenditures shares or cost shares over the period of change: (See, for example, Divisia monetary aggregates index.) The value of the index at