Some time series considerations in disaggregation

Discrete values of flow variables can be regarded as the integrals of unobserved flow functions. The estimated flows are defined as the product of two functions. One is predetermined and selected to eliminate or reduce trend in mean and variance. The other is approximately stationary, selected by smoothness criteria and the requirement that integrals of the flow reproduce the observed discrete values. Disaggregated values are obtained by integration over shorter intervals. The discrete observations contain good information about low-frequency variations of the flow. Joint analysis with related series, observed at shorter intervals, has been employed to introduce high frequency variations of disaggregated values. A fundamental weakness of this approach is that the high-frequency variations of the original series were eliminated by the integration. The relationship with the related series in the relevant frequency range cannot therefore be estimated from the data. Actual examples and comparison with other methods are presented.