The Interpolation of Time Series by Related Series

Abstract The construction of most comprehensive economic time series involves the estimation of some components for some dates by interpolation between values (“benchmarks”) for earlier and later dates. This is often done by using a related series known for all relevant dates. In practice, the bulk of such interpolation uses only a single related series, its values for only three dates—the interpolation date, one prior date, and one later date—and the values of the given series for only the prior and later dates. For this special case, some current methods are defective on formal grounds and all may frequently yield less accurate estimates than straight-line or other mathematical interpolation. Converting the problem into a simple bivariate regression problem suggests a generalization of current methods that takes account of the correlation between the movements of the given series and the related series.