A state space approach to extracting the signal from uncertain data

Most macroeconomic data are uncertain - they are estimates rather than perfect measures. Use of these uncertain data to form an assessment of current activity can be viewed as a problem of signal extraction. One symptom of that uncertainty is the propensity of statistical agencies to revise their estimates in the light of new information or methodological advances. This paper sets out an approach to extracting the signal from uncertain data that takes the experience of past revisions as representative of the uncertainties surrounding the latest published estimates. Specifically, it describes a two-step estimation procedure in which the history of past revisions (real-time data) are first used to estimate the parameters of a measurement equation describing the official published estimates; and these parameters are then imposed in a maximum likelihood estimation of a state space representation of the 'true' profile of the macroeconomic variable.