Multiple imputation of time series: an application to the construction of historical price indexes

Time series in many areas of application, and notably in the social sciences, are frequently incomplete. This is particularly annoying when we need to have complete data, for instance to compute indexes as a weighted average of values from a number of time series; whenever a single datum is absent, the index cannot be computed. This paper proposes to deal with such situations by creating multiple completed trajectories, drawing on state space modelling of time series, the simulation smoother and multiple imputation ideas.