Prediction with Incomplete Information

A key requirement for forming data-driven predictions is to assemble the best possible set of observations for the predictive variables. This task, however, is not often easy. In the case of time-series data, some variables have shorter histories than others, and some variables are reported less frequently than others. And in the case of cross-sectional data, some information is not reported for every case. We are therefore faced with several choices. We can discard predictive variables with missing information. We can exclude observations with missing information and retain only those with full information for all the predictive variables. We can use statistical techniques to manufacture replacements for the missing information. Each of these approaches, however, has significant drawbacks. The authors propose a new procedure for treating missing information that enables us to retain more information than model-based approaches and, at the same time, to account for the relative reliability of observations with missing information.